From 90cc4065d3b578997cb800c34cb1ec38c66f22cc Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Mon, 15 Jan 2018 15:14:15 +0200 Subject: [PATCH] Bessel transform mathematica results etc. Former-commit-id: 3dca9d0ccbfefa4c5f3867ce4ba31229646ca2d9 --- besseltransforms/2-1-0 | 2 ++ besseltransforms/2-1-1 | 2 ++ besseltransforms/2-1-2 | 2 ++ besseltransforms/2-1-3 | 2 ++ besseltransforms/2-1-4 | 2 ++ besseltransforms/2-1-5 | 2 ++ besseltransforms/2-1-6 | 2 ++ besseltransforms/2-1-7 | 2 ++ besseltransforms/2-2-0 | 9 +++++++++ besseltransforms/2-2-1 | 2 ++ besseltransforms/2-2-2 | 2 ++ besseltransforms/2-2-3 | 2 ++ besseltransforms/2-2-4 | 2 ++ besseltransforms/2-2-5 | 2 ++ besseltransforms/2-2-6 | 2 ++ besseltransforms/2-2-7 | 2 ++ besseltransforms/2-3-0 | 9 +++++++++ besseltransforms/2-3-1 | 9 +++++++++ besseltransforms/2-3-2 | 2 ++ besseltransforms/2-3-3 | 2 ++ besseltransforms/2-3-4 | 2 ++ besseltransforms/2-3-5 | 2 ++ besseltransforms/2-3-6 | 2 ++ besseltransforms/2-3-7 | 2 ++ besseltransforms/3-2-1 | 2 ++ besseltransforms/3-3-0 | 9 +++++++++ besseltransforms/3-3-1 | 9 +++++++++ besseltransforms/3-3-2 | 2 ++ besseltransforms/3-3-3 | 2 ++ besseltransforms/3-3-4 | 2 ++ besseltransforms/3-3-5 | 2 ++ besseltransforms/3-3-6 | 2 ++ besseltransforms/3-3-7 | 2 ++ besseltransforms/4-1-1 | 2 ++ besseltransforms/4-1-2 | 2 ++ besseltransforms/4-1-3 | 2 ++ besseltransforms/4-1-4 | 2 ++ besseltransforms/4-1-5 | 2 ++ besseltransforms/4-1-6 | 2 ++ besseltransforms/4-1-7 | 2 ++ besseltransforms/4-2-0 | 9 +++++++++ besseltransforms/4-2-1 | 0 besseltransforms/4-2-2 | 2 ++ besseltransforms/4-2-3 | 2 ++ besseltransforms/4-2-4 | 2 ++ besseltransforms/4-2-5 | 2 ++ besseltransforms/4-2-6 | 2 ++ besseltransforms/4-2-7 | 2 ++ besseltransforms/4-3-0 | 9 +++++++++ besseltransforms/4-3-1 | 9 +++++++++ besseltransforms/4-3-2 | 2 ++ besseltransforms/4-3-3 | 2 ++ besseltransforms/4-3-4 | 2 ++ besseltransforms/4-3-5 | 2 ++ besseltransforms/4-3-6 | 2 ++ besseltransforms/4-3-7 | 2 ++ besseltransforms/4-4-0 | 9 +++++++++ besseltransforms/4-4-1 | 9 +++++++++ besseltransforms/4-4-2 | 9 +++++++++ besseltransforms/4-4-3 | 2 ++ besseltransforms/4-4-4 | 2 ++ besseltransforms/4-4-5 | 2 ++ besseltransforms/4-4-6 | 2 ++ besseltransforms/4-4-7 | 2 ++ besseltransforms/5-1-0 | 2 ++ besseltransforms/5-1-1 | 2 ++ besseltransforms/5-1-2 | 2 ++ besseltransforms/5-1-3 | 2 ++ besseltransforms/5-1-4 | 2 ++ besseltransforms/5-1-5 | 2 ++ besseltransforms/5-1-6 | 2 ++ besseltransforms/5-1-7 | 2 ++ besseltransforms/5-2-0 | 9 +++++++++ besseltransforms/5-2-1 | 2 ++ besseltransforms/5-2-2 | 2 ++ besseltransforms/5-2-3 | 2 ++ besseltransforms/5-2-4 | 2 ++ besseltransforms/5-2-5 | 2 ++ besseltransforms/5-2-6 | 2 ++ besseltransforms/5-2-7 | 2 ++ besseltransforms/5-3-0 | 9 +++++++++ besseltransforms/5-3-1 | 9 +++++++++ besseltransforms/5-3-2 | 2 ++ besseltransforms/5-3-3 | 2 ++ besseltransforms/5-3-4 | 2 ++ besseltransforms/5-3-5 | 2 ++ besseltransforms/5-3-6 | 2 ++ besseltransforms/5-3-7 | 2 ++ besseltransforms/5-4-0 | 9 +++++++++ besseltransforms/5-4-1 | 9 +++++++++ besseltransforms/5-4-2 | 9 +++++++++ besseltransforms/5-4-3 | 2 ++ besseltransforms/5-4-4 | 2 ++ besseltransforms/5-4-5 | 2 ++ besseltransforms/5-4-6 | 2 ++ besseltransforms/5-4-7 | 2 ++ besseltransforms/5-5-0 | 9 +++++++++ besseltransforms/5-5-1 | 9 +++++++++ besseltransforms/5-5-2 | 9 +++++++++ besseltransforms/5-5-3 | 9 +++++++++ besseltransforms/5-5-4 | 2 ++ besseltransforms/5-5-5 | 2 ++ besseltransforms/5-5-6 | 2 ++ besseltransforms/5-5-7 | 2 ++ besseltransforms/6-1-0 | 2 ++ besseltransforms/6-1-1 | 2 ++ besseltransforms/6-1-2 | 2 ++ besseltransforms/6-1-3 | 2 ++ besseltransforms/6-1-4 | 2 ++ besseltransforms/6-1-5 | 2 ++ besseltransforms/6-1-6 | 2 ++ besseltransforms/6-1-7 | 2 ++ besseltransforms/6-2-0 | 9 +++++++++ besseltransforms/6-2-1 | 2 ++ besseltransforms/6-2-2 | 2 ++ besseltransforms/6-2-3 | 2 ++ besseltransforms/6-2-4 | 2 ++ besseltransforms/6-2-5 | 2 ++ besseltransforms/6-2-6 | 2 ++ besseltransforms/6-2-7 | 2 ++ besseltransforms/6-3-0 | 9 +++++++++ besseltransforms/6-3-1 | 9 +++++++++ besseltransforms/6-3-2 | 2 ++ besseltransforms/6-3-3 | 2 ++ besseltransforms/6-3-4 | 2 ++ besseltransforms/6-3-5 | 2 ++ besseltransforms/6-3-6 | 2 ++ besseltransforms/6-3-7 | 2 ++ besseltransforms/6-4-0 | 9 +++++++++ besseltransforms/6-4-1 | 9 +++++++++ besseltransforms/6-4-2 | 9 +++++++++ besseltransforms/6-4-3 | 2 ++ besseltransforms/6-4-4 | 2 ++ besseltransforms/6-4-5 | 2 ++ besseltransforms/6-4-6 | 2 ++ besseltransforms/6-4-7 | 2 ++ besseltransforms/6-5-0 | 9 +++++++++ besseltransforms/6-5-1 | 9 +++++++++ besseltransforms/6-5-2 | 9 +++++++++ besseltransforms/6-5-3 | 9 +++++++++ besseltransforms/6-5-4 | 2 ++ besseltransforms/6-5-5 | 2 ++ besseltransforms/6-5-6 | 2 ++ besseltransforms/6-5-7 | 2 ++ besseltransforms/7-1-0 | 2 ++ besseltransforms/7-1-1 | 2 ++ besseltransforms/7-1-2 | 2 ++ besseltransforms/7-1-3 | 2 ++ besseltransforms/7-1-4 | 2 ++ besseltransforms/7-1-5 | 2 ++ besseltransforms/7-1-6 | 2 ++ besseltransforms/7-1-7 | 2 ++ besseltransforms/7-2-0 | 9 +++++++++ besseltransforms/7-2-1 | 2 ++ besseltransforms/7-2-2 | 2 ++ besseltransforms/7-2-3 | 2 ++ besseltransforms/7-2-4 | 2 ++ besseltransforms/7-2-5 | 2 ++ besseltransforms/7-2-6 | 2 ++ besseltransforms/7-2-7 | 2 ++ besseltransforms/7-3-0 | 9 +++++++++ besseltransforms/7-3-1 | 9 +++++++++ besseltransforms/7-3-2 | 2 ++ besseltransforms/7-3-3 | 2 ++ besseltransforms/7-3-4 | 2 ++ besseltransforms/7-3-5 | 2 ++ besseltransforms/7-3-6 | 2 ++ besseltransforms/7-3-7 | 2 ++ besseltransforms/7-4-0 | 9 +++++++++ besseltransforms/7-4-1 | 9 +++++++++ besseltransforms/7-4-2 | 9 +++++++++ besseltransforms/7-4-3 | 2 ++ besseltransforms/7-4-4 | 2 ++ besseltransforms/7-4-5 | 2 ++ besseltransforms/7-4-6 | 2 ++ besseltransforms/7-4-7 | 2 ++ besseltransforms/7-5-0 | 0 besseltransforms/7-5-1 | 9 +++++++++ besseltransforms/7-5-2 | 9 +++++++++ besseltransforms/7-5-3 | 10 ++++++++++ besseltransforms/7-5-4 | 2 ++ besseltransforms/7-5-5 | 2 ++ besseltransforms/7-5-6 | 2 ++ besseltransforms/7-5-7 | 2 ++ besseltransforms/7-6-0 | 9 +++++++++ besseltransforms/7-6-1 | 9 +++++++++ besseltransforms/7-6-2 | 9 +++++++++ besseltransforms/7-6-3 | 10 ++++++++++ besseltransforms/7-6-4 | 9 +++++++++ besseltransforms/7-6-5 | 2 ++ besseltransforms/7-6-6 | 2 ++ besseltransforms/7-6-7 | 2 ++ besseltransforms/7-7-0 | 9 +++++++++ besseltransforms/7-7-1 | 9 +++++++++ besseltransforms/7-7-2 | 9 +++++++++ besseltransforms/7-7-3 | 9 +++++++++ besseltransforms/7-7-4 | 9 +++++++++ besseltransforms/7-7-5 | 10 ++++++++++ besseltransforms/7-7-6 | 2 ++ besseltransforms/7-7-7 | 2 ++ misc/finitesqlatzsym-scatter.py | 6 +++++- qpms/přehled.md | 1 + setup.py | 1 + 203 files changed, 763 insertions(+), 1 deletion(-) create mode 100644 besseltransforms/2-1-0 create mode 100644 besseltransforms/2-1-1 create mode 100644 besseltransforms/2-1-2 create mode 100644 besseltransforms/2-1-3 create mode 100644 besseltransforms/2-1-4 create mode 100644 besseltransforms/2-1-5 create mode 100644 besseltransforms/2-1-6 create mode 100644 besseltransforms/2-1-7 create mode 100644 besseltransforms/2-2-0 create mode 100644 besseltransforms/2-2-1 create mode 100644 besseltransforms/2-2-2 create mode 100644 besseltransforms/2-2-3 create mode 100644 besseltransforms/2-2-4 create mode 100644 besseltransforms/2-2-5 create mode 100644 besseltransforms/2-2-6 create mode 100644 besseltransforms/2-2-7 create mode 100644 besseltransforms/2-3-0 create mode 100644 besseltransforms/2-3-1 create mode 100644 besseltransforms/2-3-2 create mode 100644 besseltransforms/2-3-3 create mode 100644 besseltransforms/2-3-4 create mode 100644 besseltransforms/2-3-5 create mode 100644 besseltransforms/2-3-6 create mode 100644 besseltransforms/2-3-7 create mode 100644 besseltransforms/3-2-1 create mode 100644 besseltransforms/3-3-0 create mode 100644 besseltransforms/3-3-1 create mode 100644 besseltransforms/3-3-2 create mode 100644 besseltransforms/3-3-3 create mode 100644 besseltransforms/3-3-4 create mode 100644 besseltransforms/3-3-5 create mode 100644 besseltransforms/3-3-6 create mode 100644 besseltransforms/3-3-7 create mode 100644 besseltransforms/4-1-1 create mode 100644 besseltransforms/4-1-2 create mode 100644 besseltransforms/4-1-3 create mode 100644 besseltransforms/4-1-4 create mode 100644 besseltransforms/4-1-5 create mode 100644 besseltransforms/4-1-6 create mode 100644 besseltransforms/4-1-7 create mode 100644 besseltransforms/4-2-0 create mode 100644 besseltransforms/4-2-1 create mode 100644 besseltransforms/4-2-2 create mode 100644 besseltransforms/4-2-3 create mode 100644 besseltransforms/4-2-4 create mode 100644 besseltransforms/4-2-5 create mode 100644 besseltransforms/4-2-6 create mode 100644 besseltransforms/4-2-7 create mode 100644 besseltransforms/4-3-0 create mode 100644 besseltransforms/4-3-1 create mode 100644 besseltransforms/4-3-2 create mode 100644 besseltransforms/4-3-3 create mode 100644 besseltransforms/4-3-4 create mode 100644 besseltransforms/4-3-5 create mode 100644 besseltransforms/4-3-6 create mode 100644 besseltransforms/4-3-7 create mode 100644 besseltransforms/4-4-0 create mode 100644 besseltransforms/4-4-1 create mode 100644 besseltransforms/4-4-2 create mode 100644 besseltransforms/4-4-3 create mode 100644 besseltransforms/4-4-4 create mode 100644 besseltransforms/4-4-5 create mode 100644 besseltransforms/4-4-6 create mode 100644 besseltransforms/4-4-7 create mode 100644 besseltransforms/5-1-0 create mode 100644 besseltransforms/5-1-1 create mode 100644 besseltransforms/5-1-2 create mode 100644 besseltransforms/5-1-3 create mode 100644 besseltransforms/5-1-4 create mode 100644 besseltransforms/5-1-5 create mode 100644 besseltransforms/5-1-6 create mode 100644 besseltransforms/5-1-7 create mode 100644 besseltransforms/5-2-0 create mode 100644 besseltransforms/5-2-1 create mode 100644 besseltransforms/5-2-2 create mode 100644 besseltransforms/5-2-3 create mode 100644 besseltransforms/5-2-4 create mode 100644 besseltransforms/5-2-5 create mode 100644 besseltransforms/5-2-6 create mode 100644 besseltransforms/5-2-7 create mode 100644 besseltransforms/5-3-0 create mode 100644 besseltransforms/5-3-1 create mode 100644 besseltransforms/5-3-2 create mode 100644 besseltransforms/5-3-3 create mode 100644 besseltransforms/5-3-4 create mode 100644 besseltransforms/5-3-5 create mode 100644 besseltransforms/5-3-6 create mode 100644 besseltransforms/5-3-7 create mode 100644 besseltransforms/5-4-0 create mode 100644 besseltransforms/5-4-1 create mode 100644 besseltransforms/5-4-2 create mode 100644 besseltransforms/5-4-3 create mode 100644 besseltransforms/5-4-4 create mode 100644 besseltransforms/5-4-5 create mode 100644 besseltransforms/5-4-6 create mode 100644 besseltransforms/5-4-7 create mode 100644 besseltransforms/5-5-0 create mode 100644 besseltransforms/5-5-1 create mode 100644 besseltransforms/5-5-2 create mode 100644 besseltransforms/5-5-3 create mode 100644 besseltransforms/5-5-4 create mode 100644 besseltransforms/5-5-5 create mode 100644 besseltransforms/5-5-6 create mode 100644 besseltransforms/5-5-7 create mode 100644 besseltransforms/6-1-0 create mode 100644 besseltransforms/6-1-1 create mode 100644 besseltransforms/6-1-2 create mode 100644 besseltransforms/6-1-3 create mode 100644 besseltransforms/6-1-4 create mode 100644 besseltransforms/6-1-5 create mode 100644 besseltransforms/6-1-6 create mode 100644 besseltransforms/6-1-7 create mode 100644 besseltransforms/6-2-0 create mode 100644 besseltransforms/6-2-1 create mode 100644 besseltransforms/6-2-2 create mode 100644 besseltransforms/6-2-3 create mode 100644 besseltransforms/6-2-4 create mode 100644 besseltransforms/6-2-5 create mode 100644 besseltransforms/6-2-6 create mode 100644 besseltransforms/6-2-7 create mode 100644 besseltransforms/6-3-0 create mode 100644 besseltransforms/6-3-1 create mode 100644 besseltransforms/6-3-2 create mode 100644 besseltransforms/6-3-3 create mode 100644 besseltransforms/6-3-4 create mode 100644 besseltransforms/6-3-5 create mode 100644 besseltransforms/6-3-6 create mode 100644 besseltransforms/6-3-7 create mode 100644 besseltransforms/6-4-0 create mode 100644 besseltransforms/6-4-1 create mode 100644 besseltransforms/6-4-2 create mode 100644 besseltransforms/6-4-3 create mode 100644 besseltransforms/6-4-4 create mode 100644 besseltransforms/6-4-5 create mode 100644 besseltransforms/6-4-6 create mode 100644 besseltransforms/6-4-7 create mode 100644 besseltransforms/6-5-0 create mode 100644 besseltransforms/6-5-1 create mode 100644 besseltransforms/6-5-2 create mode 100644 besseltransforms/6-5-3 create mode 100644 besseltransforms/6-5-4 create mode 100644 besseltransforms/6-5-5 create mode 100644 besseltransforms/6-5-6 create mode 100644 besseltransforms/6-5-7 create mode 100644 besseltransforms/7-1-0 create mode 100644 besseltransforms/7-1-1 create mode 100644 besseltransforms/7-1-2 create mode 100644 besseltransforms/7-1-3 create mode 100644 besseltransforms/7-1-4 create mode 100644 besseltransforms/7-1-5 create mode 100644 besseltransforms/7-1-6 create mode 100644 besseltransforms/7-1-7 create mode 100644 besseltransforms/7-2-0 create mode 100644 besseltransforms/7-2-1 create mode 100644 besseltransforms/7-2-2 create mode 100644 besseltransforms/7-2-3 create mode 100644 besseltransforms/7-2-4 create mode 100644 besseltransforms/7-2-5 create mode 100644 besseltransforms/7-2-6 create mode 100644 besseltransforms/7-2-7 create mode 100644 besseltransforms/7-3-0 create mode 100644 besseltransforms/7-3-1 create mode 100644 besseltransforms/7-3-2 create mode 100644 besseltransforms/7-3-3 create mode 100644 besseltransforms/7-3-4 create mode 100644 besseltransforms/7-3-5 create mode 100644 besseltransforms/7-3-6 create mode 100644 besseltransforms/7-3-7 create mode 100644 besseltransforms/7-4-0 create mode 100644 besseltransforms/7-4-1 create mode 100644 besseltransforms/7-4-2 create mode 100644 besseltransforms/7-4-3 create mode 100644 besseltransforms/7-4-4 create mode 100644 besseltransforms/7-4-5 create mode 100644 besseltransforms/7-4-6 create mode 100644 besseltransforms/7-4-7 create mode 100644 besseltransforms/7-5-0 create mode 100644 besseltransforms/7-5-1 create mode 100644 besseltransforms/7-5-2 create mode 100644 besseltransforms/7-5-3 create mode 100644 besseltransforms/7-5-4 create mode 100644 besseltransforms/7-5-5 create mode 100644 besseltransforms/7-5-6 create mode 100644 besseltransforms/7-5-7 create mode 100644 besseltransforms/7-6-0 create mode 100644 besseltransforms/7-6-1 create mode 100644 besseltransforms/7-6-2 create mode 100644 besseltransforms/7-6-3 create mode 100644 besseltransforms/7-6-4 create mode 100644 besseltransforms/7-6-5 create mode 100644 besseltransforms/7-6-6 create mode 100644 besseltransforms/7-6-7 create mode 100644 besseltransforms/7-7-0 create mode 100644 besseltransforms/7-7-1 create mode 100644 besseltransforms/7-7-2 create mode 100644 besseltransforms/7-7-3 create mode 100644 besseltransforms/7-7-4 create mode 100644 besseltransforms/7-7-5 create mode 100644 besseltransforms/7-7-6 create mode 100644 besseltransforms/7-7-7 diff --git a/besseltransforms/2-1-0 b/besseltransforms/2-1-0 new file mode 100644 index 0000000..2c6e1ee --- /dev/null +++ b/besseltransforms/2-1-0 @@ -0,0 +1,2 @@ +(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 2/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/k0 +SeriesData[k, Infinity, {-(c^2/(k*k0)), 0, (3*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (-5*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (35*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k*k0), 0, (-63*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-1 b/besseltransforms/2-1-1 new file mode 100644 index 0000000..d4bbdaa --- /dev/null +++ b/besseltransforms/2-1-1 @@ -0,0 +1,2 @@ +-((-2 + 2*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]) + 1/Sqrt[1 + k^2/(c - I*k0)^2] + 1/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k*k0)) +SeriesData[k, Infinity, {(3*(2*c^3 - I*c^2*k0))/(k*k0), 0, (-15*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (35*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k*k0), 0, (-105*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 3, 11, 1] diff --git a/besseltransforms/2-1-2 b/besseltransforms/2-1-2 new file mode 100644 index 0000000..e4532d3 --- /dev/null +++ b/besseltransforms/2-1-2 @@ -0,0 +1,2 @@ +(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 2/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (6*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (-6*c + (2*I)*k0)/k^2 + (8*c - (4*I)*k0)/k^2 + (-8*c + (4*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(3*c^2)/(k*k0), 0, (-5*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (-45*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k*k0), 0, (77*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-3 b/besseltransforms/2-1-3 new file mode 100644 index 0000000..b9ff315 --- /dev/null +++ b/besseltransforms/2-1-3 @@ -0,0 +1,2 @@ +((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^3*k0) +SeriesData[k, Infinity, {(8*c^2)/(k*k0), (-15*(2*c^3 - I*c^2*k0))/(k*k0), 0, (35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (63*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (165*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-4 b/besseltransforms/2-1-4 new file mode 100644 index 0000000..0eb249d --- /dev/null +++ b/besseltransforms/2-1-4 @@ -0,0 +1,2 @@ +((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^4*k0) +SeriesData[k, Infinity, {(15*c^2)/(k*k0), (-48*(2*c^3 - I*c^2*k0))/(k*k0), (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (-21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (-99*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (-143*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-5 b/besseltransforms/2-1-5 new file mode 100644 index 0000000..2061c66 --- /dev/null +++ b/besseltransforms/2-1-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^5*k0) +SeriesData[k, Infinity, {(24*c^2)/(k*k0), (-105*(2*c^3 - I*c^2*k0))/(k*k0), (32*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (231*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k*k0), 0, (429*(-3110*c^9 + (9075*I)*c^8*k0 + 11592*c^7*k0^2 - (8428*I)*c^6*k0^3 - 3780*c^5*k0^4 + (1050*I)*c^4*k0^5 + 168*c^3*k0^6 - (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-6 b/besseltransforms/2-1-6 new file mode 100644 index 0000000..900e941 --- /dev/null +++ b/besseltransforms/2-1-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^6*k0) +SeriesData[k, Infinity, {(35*c^2)/(k*k0), (-192*(2*c^3 - I*c^2*k0))/(k*k0), (315*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), (-320*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(k*k0), (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (429*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (429*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-1-7 b/besseltransforms/2-1-7 new file mode 100644 index 0000000..b576a37 --- /dev/null +++ b/besseltransforms/2-1-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^7*k0) +SeriesData[k, Infinity, {(48*c^2)/(k*k0), (-315*(2*c^3 - I*c^2*k0))/(k*k0), (160*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-3465*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), (128*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(k*k0), (3003*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (2145*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1] diff --git a/besseltransforms/2-2-0 b/besseltransforms/2-2-0 new file mode 100644 index 0000000..eb7788f --- /dev/null +++ b/besseltransforms/2-2-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -3 c x + I k0 x c x 2 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 2 21/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/2-2-1 b/besseltransforms/2-2-1 new file mode 100644 index 0000000..290b99a --- /dev/null +++ b/besseltransforms/2-2-1 @@ -0,0 +1,2 @@ +((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/(k*k0^2) +SeriesData[k, Infinity, {c^2/k0^2, 0, (3*c^2)/2 - (25*c^4)/(4*k0^2) + ((6*I)*c^3)/k0, 0, (301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4)/(8*k0^2), 0, (-5*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (7*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-2 b/besseltransforms/2-2-2 new file mode 100644 index 0000000..42245d6 --- /dev/null +++ b/besseltransforms/2-2-2 @@ -0,0 +1,2 @@ +-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/(k^2*k0^2)) +SeriesData[k, Infinity, {(2*c^2)/k0^2, (-6*c^3)/k0^2 + ((3*I)*c^2)/k0, 0, -15*c^3 + (45*c^5)/(2*k0^2) - ((125*I)/4*c^4)/k0 + (5*I)/2*c^2*k0, 0, (-7*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (15*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-3 b/besseltransforms/2-2-3 new file mode 100644 index 0000000..d78923c --- /dev/null +++ b/besseltransforms/2-2-3 @@ -0,0 +1,2 @@ +(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 2*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^3*k0^2) +SeriesData[k, Infinity, {(3*c^2)/k0^2, (-16*c^3)/k0^2 + ((8*I)*c^2)/k0, (-15*c^2)/2 + (125*c^4)/(4*k0^2) - ((30*I)*c^3)/k0, 0, (-7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^2), 0, (9*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (-11*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-4 b/besseltransforms/2-2-4 new file mode 100644 index 0000000..3da9cf6 --- /dev/null +++ b/besseltransforms/2-2-4 @@ -0,0 +1,2 @@ +-(2*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 2*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(2*k^4*k0^2) +SeriesData[k, Infinity, {(4*c^2)/k0^2, (-30*c^3)/k0^2 + ((15*I)*c^2)/k0, -24*c^2 + (100*c^4)/k0^2 - ((96*I)*c^3)/k0, 105*c^3 - (315*c^5)/(2*k0^2) + ((875*I)/4*c^4)/k0 - (35*I)/2*c^2*k0, 0, (21*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (-33*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-5 b/besseltransforms/2-2-5 new file mode 100644 index 0000000..39aa789 --- /dev/null +++ b/besseltransforms/2-2-5 @@ -0,0 +1,2 @@ +(-2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(5*k^5*k0^2) +SeriesData[k, Infinity, {(5*c^2)/k0^2, (-24*(2*c^3 - I*c^2*k0))/k0^2, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-32*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), 0, ((-165*(c - I*k0)^8)/128 + (165*(2*c - I*k0)^8)/64 - (165*(3*c - I*k0)^8)/128)/(5*k0^2), 0, ((143*(c - I*k0)^10)/256 - (143*(2*c - I*k0)^10)/128 + (143*(3*c - I*k0)^10)/256)/(5*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-6 b/besseltransforms/2-2-6 new file mode 100644 index 0000000..edf6ace --- /dev/null +++ b/besseltransforms/2-2-6 @@ -0,0 +1,2 @@ +(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(3*k^6*k0^2) +SeriesData[k, Infinity, {(6*c^2)/k0^2, (-35*(2*c^3 - I*c^2*k0))/k0^2, (16*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^2, (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), (16*(c - I*k0)^6 - 32*(2*c - I*k0)^6 + 16*(3*c - I*k0)^6)/(3*k0^2), ((-99*(c - I*k0)^7)/16 + (99*(2*c - I*k0)^7)/8 - (99*(3*c - I*k0)^7)/16)/(3*k0^2), 0, ((143*(c - I*k0)^9)/128 - (143*(2*c - I*k0)^9)/64 + (143*(3*c - I*k0)^9)/128)/(3*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-2-7 b/besseltransforms/2-2-7 new file mode 100644 index 0000000..ee5cf53 --- /dev/null +++ b/besseltransforms/2-2-7 @@ -0,0 +1,2 @@ +(-2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(7*k^7*k0^2) +SeriesData[k, Infinity, {(7*c^2)/k0^2, (-48*(2*c^3 - I*c^2*k0))/k0^2, (105*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-160*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), (-64*(c - I*k0)^7 + 128*(2*c - I*k0)^7 - 64*(3*c - I*k0)^7)/(7*k0^2), ((3003*(c - I*k0)^8)/128 - (3003*(2*c - I*k0)^8)/64 + (3003*(3*c - I*k0)^8)/128)/(7*k0^2), 0, ((-1001*(c - I*k0)^10)/256 + (1001*(2*c - I*k0)^10)/128 - (1001*(3*c - I*k0)^10)/256)/(7*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-3-0 b/besseltransforms/2-3-0 new file mode 100644 index 0000000..14287a6 --- /dev/null +++ b/besseltransforms/2-3-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -3 c x + I k0 x c x 2 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/2-3-1 b/besseltransforms/2-3-1 new file mode 100644 index 0000000..125bafb --- /dev/null +++ b/besseltransforms/2-3-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -3 c x + I k0 x c x 2 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/2-3-2 b/besseltransforms/2-3-2 new file mode 100644 index 0000000..78fb0ed --- /dev/null +++ b/besseltransforms/2-3-2 @@ -0,0 +1,2 @@ +((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 - 2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - (4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + (-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2)/(6*k0^3) +SeriesData[k, Infinity, {c^2/k0^3, (-4*c^3)/k0^3 + ((2*I)*c^2)/k0^2, (25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2)/(4*k0^3), 0, (-301*c^6 + (540*I)*c^5*k0 + 375*c^4*k0^2 - (120*I)*c^3*k0^3 - 15*c^2*k0^4)/(24*k0^3), 0, (3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6)/(64*k0^3), 0, (-28501*c^10 + (93300*I)*c^9*k0 + 136125*c^8*k0^2 - (115920*I)*c^7*k0^3 - 63210*c^6*k0^4 + (22680*I)*c^5*k0^5 + 5250*c^4*k0^6 - (720*I)*c^3*k0^7 - 45*c^2*k0^8)/(128*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-3 b/besseltransforms/2-3-3 new file mode 100644 index 0000000..99e8566 --- /dev/null +++ b/besseltransforms/2-3-3 @@ -0,0 +1,2 @@ +(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(6*k^3*k0^3) +SeriesData[k, Infinity, {c^2/k0^3, (-3*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(3*k0^3), (-5*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), 0, ((c - I*k0)^7/8 - (2*c - I*k0)^7/4 + (3*c - I*k0)^7/8)/(6*k0^3), 0, ((-3*(c - I*k0)^9)/64 + (3*(2*c - I*k0)^9)/32 - (3*(3*c - I*k0)^9)/64)/(6*k0^3), 0, ((3*(c - I*k0)^11)/128 - (3*(2*c - I*k0)^11)/64 + (3*(3*c - I*k0)^11)/128)/(6*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-4 b/besseltransforms/2-3-4 new file mode 100644 index 0000000..f7f8b9b --- /dev/null +++ b/besseltransforms/2-3-4 @@ -0,0 +1,2 @@ +(-2*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(60*k^4*k0^3) +SeriesData[k, Infinity, {c^2/k0^3, (-4*(2*c^3 - I*c^2*k0))/k0^3, (5*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^3), (-4*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^3), 0, ((-45*(c - I*k0)^8)/32 + (45*(2*c - I*k0)^8)/16 - (45*(3*c - I*k0)^8)/32)/(60*k0^3), 0, ((33*(c - I*k0)^10)/64 - (33*(2*c - I*k0)^10)/32 + (33*(3*c - I*k0)^10)/64)/(60*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-5 b/besseltransforms/2-3-5 new file mode 100644 index 0000000..19de25b --- /dev/null +++ b/besseltransforms/2-3-5 @@ -0,0 +1,2 @@ +(6*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 6*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(60*k^5*k0^3) +SeriesData[k, Infinity, {c^2/k0^3, (-5*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (32*(c - I*k0)^6 - 64*(2*c - I*k0)^6 + 32*(3*c - I*k0)^6)/(60*k0^3), ((-45*(c - I*k0)^7)/4 + (45*(2*c - I*k0)^7)/2 - (45*(3*c - I*k0)^7)/4)/(60*k0^3), 0, ((55*(c - I*k0)^9)/32 - (55*(2*c - I*k0)^9)/16 + (55*(3*c - I*k0)^9)/32)/(60*k0^3), 0, ((-39*(c - I*k0)^11)/64 + (39*(2*c - I*k0)^11)/32 - (39*(3*c - I*k0)^11)/64)/(60*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-6 b/besseltransforms/2-3-6 new file mode 100644 index 0000000..36b5ad4 --- /dev/null +++ b/besseltransforms/2-3-6 @@ -0,0 +1,2 @@ +(-2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(210*k^6*k0^3) +SeriesData[k, Infinity, {c^2/k0^3, (-6*(2*c^3 - I*c^2*k0))/k0^3, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(12*k0^3), (-16*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^3), (-160*(c - I*k0)^7 + 320*(2*c - I*k0)^7 - 160*(3*c - I*k0)^7)/(210*k0^3), ((3465*(c - I*k0)^8)/64 - (3465*(2*c - I*k0)^8)/32 + (3465*(3*c - I*k0)^8)/64)/(210*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (1001*(2*c - I*k0)^10)/64 - (1001*(3*c - I*k0)^10)/128)/(210*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/2-3-7 b/besseltransforms/2-3-7 new file mode 100644 index 0000000..cae73a7 --- /dev/null +++ b/besseltransforms/2-3-7 @@ -0,0 +1,2 @@ +((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(168*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(336*k^7))/k0^3 +SeriesData[k, Infinity, {c^2/k0^3, (-7*(2*c^3 - I*c^2*k0))/k0^3, (4*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-105*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (16*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(3*k0^3), ((-33*(c - I*k0)^7)/16 + (33*(2*c - I*k0)^7)/8 - (33*(3*c - I*k0)^7)/16)/k0^3, ((8*(c - I*k0)^8)/7 - (16*(2*c - I*k0)^8)/7 + (8*(3*c - I*k0)^8)/7)/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/192 - (143*(3*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (13*(2*c - I*k0)^11)/128 + (13*(3*c - I*k0)^11)/256)/k0^3}, 1, 11, 1] diff --git a/besseltransforms/3-2-1 b/besseltransforms/3-2-1 new file mode 100644 index 0000000..a49536b --- /dev/null +++ b/besseltransforms/3-2-1 @@ -0,0 +1,2 @@ +((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 3*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 3*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/(k*k0^2) +SeriesData[k, Infinity, {(15*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^2), 0, (-105*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/3-3-0 b/besseltransforms/3-3-0 new file mode 100644 index 0000000..f679ead --- /dev/null +++ b/besseltransforms/3-3-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -4 c x + I k0 x c x 3 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/3-3-1 b/besseltransforms/3-3-1 new file mode 100644 index 0000000..a06b92b --- /dev/null +++ b/besseltransforms/3-3-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -4 c x + I k0 x c x 3 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/3-3-2 b/besseltransforms/3-3-2 new file mode 100644 index 0000000..7a2c082 --- /dev/null +++ b/besseltransforms/3-3-2 @@ -0,0 +1,2 @@ +((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 3*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 3*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + (6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2)/(6*k0^3) +SeriesData[k, Infinity, {(2*c^3)/k0^3, (-15*c^4)/(2*k0^3) + ((3*I)*c^3)/k0^2, 0, (5*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (-21*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (15*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-3 b/besseltransforms/3-3-3 new file mode 100644 index 0000000..481d01d --- /dev/null +++ b/besseltransforms/3-3-3 @@ -0,0 +1,2 @@ +(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 3*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 3*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/(6*k^3*k0^3) +SeriesData[k, Infinity, {(3*c^3)/k0^3, (-20*c^4)/k0^3 + ((8*I)*c^3)/k0^2, (15*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), 0, (-7*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (3*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, (-33*(55591*c^11 - (145750*I)*c^10*k0 - 170525*c^9*k0^2 + (116550*I)*c^8*k0^3 + 51030*c^7*k0^4 - (14700*I)*c^6*k0^5 - 2730*c^5*k0^6 + (300*I)*c^4*k0^7 + 15*c^3*k0^8))/(128*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-4 b/besseltransforms/3-3-4 new file mode 100644 index 0000000..eab2da8 --- /dev/null +++ b/besseltransforms/3-3-4 @@ -0,0 +1,2 @@ +(-3*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 3*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 - k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(60*k^4*k0^3) +SeriesData[k, Infinity, {(4*c^3)/k0^3, (-75*c^4)/(2*k0^3) + ((15*I)*c^3)/k0^2, (156*c^5)/k0^3 - ((120*I)*c^4)/k0^2 - (24*c^3)/k0, (-35*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (63*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (-33*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-5 b/besseltransforms/3-3-5 new file mode 100644 index 0000000..a508a6b --- /dev/null +++ b/besseltransforms/3-3-5 @@ -0,0 +1,2 @@ +(3*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 9*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 48*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 9*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 6*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 48*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5*k0^3) +SeriesData[k, Infinity, {(5*c^3)/k0^3, (-12*(5*c^4 - (2*I)*c^3*k0))/k0^3, (105*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-32*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (63*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (-11*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, ((-39*(c - I*k0)^11)/128 + (117*(2*c - I*k0)^11)/128 - (117*(3*c - I*k0)^11)/128 + (39*(4*c - I*k0)^11)/128)/(30*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-6 b/besseltransforms/3-3-6 new file mode 100644 index 0000000..eb3a4ac --- /dev/null +++ b/besseltransforms/3-3-6 @@ -0,0 +1,2 @@ +(-3*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 3*(k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 - k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 - 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^6*k0^3) +SeriesData[k, Infinity, {(6*c^3)/k0^3, (-35*(5*c^4 - (2*I)*c^3*k0))/(2*k0^3), (48*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/k0^3, (-315*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), (32*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/k0^3, (-693*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (3003*(2*c - I*k0)^10)/128 - (3003*(3*c - I*k0)^10)/128 + (1001*(4*c - I*k0)^10)/128)/(210*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/3-3-7 b/besseltransforms/3-3-7 new file mode 100644 index 0000000..73e7bdb --- /dev/null +++ b/besseltransforms/3-3-7 @@ -0,0 +1,2 @@ +((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(112*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(112*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(336*k^7))/k0^3 +SeriesData[k, Infinity, {(7*c^3)/k0^3, (-24*(5*c^4 - (2*I)*c^3*k0))/k0^3, (315*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-160*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (693*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), (-96*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/128 - (143*(3*c - I*k0)^9)/128 + (143*(4*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (39*(2*c - I*k0)^11)/256 + (39*(3*c - I*k0)^11)/256 - (13*(4*c - I*k0)^11)/256)/k0^3}, 2, 11, 1] diff --git a/besseltransforms/4-1-1 b/besseltransforms/4-1-1 new file mode 100644 index 0000000..e162607 --- /dev/null +++ b/besseltransforms/4-1-1 @@ -0,0 +1,2 @@ +(2/k - 4*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 6*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 4*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((45*I)*c^4)/k - (135*c^5)/(k*k0), 0, (525*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (-2205*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/4-1-2 b/besseltransforms/4-1-2 new file mode 100644 index 0000000..f6793b6 --- /dev/null +++ b/besseltransforms/4-1-2 @@ -0,0 +1,2 @@ +(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 4/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 6/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (12*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) - 4/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (-10*c + (2*I)*k0)/k^2 + (16*c - (8*I)*k0)/k^2 + (32*c - (8*I)*k0)/k^2 + (-32*c + (8*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-16*c + (8*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-36*c + (12*I)*k0)/k^2)/k0 +SeriesData[k, Infinity, {(-15*c^4)/(k*k0), 0, (105*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (-945*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (1155*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-3 b/besseltransforms/4-1-3 new file mode 100644 index 0000000..3bbfe99 --- /dev/null +++ b/besseltransforms/4-1-3 @@ -0,0 +1,2 @@ +((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((-105*I)*c^4)/k + (315*c^5)/(k*k0), 0, (-945*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (3465*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/4-1-4 b/besseltransforms/4-1-4 new file mode 100644 index 0000000..ff93fca --- /dev/null +++ b/besseltransforms/4-1-4 @@ -0,0 +1,2 @@ +((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0 +SeriesData[k, Infinity, {(105*c^4)/(k*k0), 0, (-315*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (2079*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-5 b/besseltransforms/4-1-5 new file mode 100644 index 0000000..dba2345 --- /dev/null +++ b/besseltransforms/4-1-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(384*c^4)/(k*k0), ((945*I)*c^4)/k - (2835*c^5)/(k*k0), 0, (3465*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (-9009*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-6 b/besseltransforms/4-1-6 new file mode 100644 index 0000000..73f1ea6 --- /dev/null +++ b/besseltransforms/4-1-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0 +SeriesData[k, Infinity, {(945*c^4)/(k*k0), ((3840*I)*c^4)/k - (11520*c^5)/(k*k0), (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (-9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (6435*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-1-7 b/besseltransforms/4-1-7 new file mode 100644 index 0000000..fd7b764 --- /dev/null +++ b/besseltransforms/4-1-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(1920*c^4)/(k*k0), ((10395*I)*c^4)/k - (31185*c^5)/(k*k0), (7680*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(k*k0), (-45045*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (45045*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1] diff --git a/besseltransforms/4-2-0 b/besseltransforms/4-2-0 new file mode 100644 index 0000000..d8121c9 --- /dev/null +++ b/besseltransforms/4-2-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 2 21/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-2-1 b/besseltransforms/4-2-1 new file mode 100644 index 0000000..e69de29 diff --git a/besseltransforms/4-2-2 b/besseltransforms/4-2-2 new file mode 100644 index 0000000..a457fb2 --- /dev/null +++ b/besseltransforms/4-2-2 @@ -0,0 +1,2 @@ +-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^2*k0^2)) +SeriesData[k, Infinity, {(45*c^5)/k0^2 - ((15*I)*c^4)/k0, 0, (945*c^5)/2 - (1575*c^7)/k0^2 + ((1470*I)*c^6)/k0 - (105*I)/2*c^4*k0, 0, (315*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/4-2-3 b/besseltransforms/4-2-3 new file mode 100644 index 0000000..00c163d --- /dev/null +++ b/besseltransforms/4-2-3 @@ -0,0 +1,2 @@ +(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3*k0^2) +SeriesData[k, Infinity, {(15*c^4)/k0^2, 0, (105*c^4)/2 - (490*c^6)/k0^2 + ((315*I)*c^5)/k0, 0, -6615*c^6 + (187677*c^8)/(16*k0^2) - ((14175*I)*c^7)/k0 + (2835*I)/2*c^5*k0 + (945*c^4*k0^2)/8, 0, (-165*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-4 b/besseltransforms/4-2-4 new file mode 100644 index 0000000..e20a9a3 --- /dev/null +++ b/besseltransforms/4-2-4 @@ -0,0 +1,2 @@ +-((k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*k0^2)) +SeriesData[k, Infinity, {(48*c^4)/k0^2, (-315*c^5)/k0^2 + ((105*I)*c^4)/k0, 0, (-2835*c^5)/2 + (4725*c^7)/k0^2 - ((4410*I)*c^6)/k0 + (315*I)/2*c^4*k0, 0, (-693*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-5 b/besseltransforms/4-2-5 new file mode 100644 index 0000000..42dda30 --- /dev/null +++ b/besseltransforms/4-2-5 @@ -0,0 +1,2 @@ +(-4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5*k0^2) +SeriesData[k, Infinity, {(105*c^4)/k0^2, (-1152*c^5)/k0^2 + ((384*I)*c^4)/k0, (-945*c^4)/2 + (4410*c^6)/k0^2 - ((2835*I)*c^5)/k0, 0, 24255*c^6 - (688149*c^8)/(16*k0^2) + ((51975*I)*c^7)/k0 - (10395*I)/2*c^5*k0 - (3465*c^4*k0^2)/8, 0, (429*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-6 b/besseltransforms/4-2-6 new file mode 100644 index 0000000..09ab4c6 --- /dev/null +++ b/besseltransforms/4-2-6 @@ -0,0 +1,2 @@ +(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 18*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 48*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 96*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(3*k^6*k0^2) +SeriesData[k, Infinity, {(192*c^4)/k0^2, (-2835*c^5)/k0^2 + ((945*I)*c^4)/k0, -1920*c^4 + (17920*c^6)/k0^2 - ((11520*I)*c^5)/k0, (31185*c^5)/2 - (51975*c^7)/k0^2 + ((48510*I)*c^6)/k0 - (3465*I)/2*c^4*k0, 0, (3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-2-7 b/besseltransforms/4-2-7 new file mode 100644 index 0000000..68ec2cc --- /dev/null +++ b/besseltransforms/4-2-7 @@ -0,0 +1,2 @@ +(-4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(7*k^7*k0^2) +SeriesData[k, Infinity, {(315*c^4)/k0^2, (-1920*(3*c^5 - I*c^4*k0))/k0^2, (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^2), (-7680*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^2, (9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^2), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1] diff --git a/besseltransforms/4-3-0 b/besseltransforms/4-3-0 new file mode 100644 index 0000000..25f3059 --- /dev/null +++ b/besseltransforms/4-3-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-3-1 b/besseltransforms/4-3-1 new file mode 100644 index 0000000..537e02d --- /dev/null +++ b/besseltransforms/4-3-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-3-2 b/besseltransforms/4-3-2 new file mode 100644 index 0000000..e5a281e --- /dev/null +++ b/besseltransforms/4-3-2 @@ -0,0 +1,2 @@ +(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(6*k^2*k0^3) +SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-70*c^6)/k0^3 + ((45*I)*c^5)/k0^2 + (15*c^4)/(2*k0), 0, (315*I)/2*c^5 + (20853*c^8)/(16*k0^3) - ((1575*I)*c^7)/k0^2 - (735*c^6)/k0 + (105*c^4*k0)/8, 0, (-15*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-3 b/besseltransforms/4-3-3 new file mode 100644 index 0000000..6b9f3e5 --- /dev/null +++ b/besseltransforms/4-3-3 @@ -0,0 +1,2 @@ +(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(6*k^3*k0^3) +SeriesData[k, Infinity, {(8*c^4)/k0^3, (-45*c^5)/k0^3 + ((15*I)*c^4)/k0^2, 0, (35*I)/2*c^4 + (525*c^7)/k0^3 - ((490*I)*c^6)/k0^2 - (315*c^5)/(2*k0), 0, (-63*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (165*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-4 b/besseltransforms/4-3-4 new file mode 100644 index 0000000..e2fc380 --- /dev/null +++ b/besseltransforms/4-3-4 @@ -0,0 +1,2 @@ +(-4*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(60*k^4*k0^3) +SeriesData[k, Infinity, {(15*c^4)/k0^3, (-48*(3*c^5 - I*c^4*k0))/k0^3, (35*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (-63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^3), 0, (33*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-5 b/besseltransforms/4-3-5 new file mode 100644 index 0000000..bafde08 --- /dev/null +++ b/besseltransforms/4-3-5 @@ -0,0 +1,2 @@ +((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(20*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5))/k0^3 +SeriesData[k, Infinity, {(24*c^4)/k0^3, (-315*c^5)/k0^3 + ((105*I)*c^4)/k0^2, (1792*c^6)/k0^3 - ((1152*I)*c^5)/k0^2 - (192*c^4)/k0, (-315*I)/2*c^4 - (4725*c^7)/k0^3 + ((4410*I)*c^6)/k0^2 + (2835*c^5)/(2*k0), 0, (231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (-429*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-6 b/besseltransforms/4-3-6 new file mode 100644 index 0000000..4ff87d3 --- /dev/null +++ b/besseltransforms/4-3-6 @@ -0,0 +1,2 @@ +((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(35*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(210*k^6))/k0^3 +SeriesData[k, Infinity, {(35*c^4)/k0^3, (-576*c^5)/k0^3 + ((192*I)*c^4)/k0^2, (4410*c^6)/k0^3 - ((2835*I)*c^5)/k0^2 - (945*c^4)/(2*k0), (-640*I)*c^4 - (19200*c^7)/k0^3 + ((17920*I)*c^6)/k0^2 + (5760*c^5)/k0, (10395*I)/2*c^5 + (688149*c^8)/(16*k0^3) - ((51975*I)*c^7)/k0^2 - (24255*c^6)/k0 + (3465*c^4*k0)/8, 0, (-143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-3-7 b/besseltransforms/4-3-7 new file mode 100644 index 0000000..532099c --- /dev/null +++ b/besseltransforms/4-3-7 @@ -0,0 +1,2 @@ +((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(56*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(336*k^7))/k0^3 +SeriesData[k, Infinity, {(48*c^4)/k0^3, (-945*c^5)/k0^3 + ((315*I)*c^4)/k0^2, (8960*c^6)/k0^3 - ((5760*I)*c^5)/k0^2 - (960*c^4)/k0, (-3465*I)/2*c^4 - (51975*c^7)/k0^3 + ((48510*I)*c^6)/k0^2 + (31185*c^5)/(2*k0), (23040*I)*c^5 + (190656*c^8)/k0^3 - ((230400*I)*c^7)/k0^2 - (107520*c^6)/k0 + 1920*c^4*k0, (-3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (2145*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/4-4-0 b/besseltransforms/4-4-0 new file mode 100644 index 0000000..def0ce6 --- /dev/null +++ b/besseltransforms/4-4-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-4-1 b/besseltransforms/4-4-1 new file mode 100644 index 0000000..54ab46a --- /dev/null +++ b/besseltransforms/4-4-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-4-2 b/besseltransforms/4-4-2 new file mode 100644 index 0000000..b12fe80 --- /dev/null +++ b/besseltransforms/4-4-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) + 4 +Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/4-4-3 b/besseltransforms/4-4-3 new file mode 100644 index 0000000..203d301 --- /dev/null +++ b/besseltransforms/4-4-3 @@ -0,0 +1,2 @@ +(-4*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3*k0^4) +SeriesData[k, Infinity, {(3*c^4)/k0^4, (-8*(3*c^5 - I*c^4*k0))/k0^4, (5*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), 0, (-7*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (3*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-5*(c - I*k0)^12)/128 + (5*(2*c - I*k0)^12)/32 - (15*(3*c - I*k0)^12)/64 + (5*(4*c - I*k0)^12)/32 - (5*(5*c - I*k0)^12)/128)/(120*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-4 b/besseltransforms/4-4-4 new file mode 100644 index 0000000..b9f00a9 --- /dev/null +++ b/besseltransforms/4-4-4 @@ -0,0 +1,2 @@ +((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(40*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(240*k^4))/k0^4 +SeriesData[k, Infinity, {(4*c^4)/k0^4, (-45*c^5)/k0^4 + ((15*I)*c^4)/k0^3, (224*c^6)/k0^4 - ((144*I)*c^5)/k0^3 - (24*c^4)/k0^2, (-35*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 0, (21*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (-33*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-5 b/besseltransforms/4-4-5 new file mode 100644 index 0000000..b225d16 --- /dev/null +++ b/besseltransforms/4-4-5 @@ -0,0 +1,2 @@ +((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(140*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5))/k0^4 +SeriesData[k, Infinity, {(5*c^4)/k0^4, (-72*c^5)/k0^4 + ((24*I)*c^4)/k0^3, (490*c^6)/k0^4 - ((315*I)*c^5)/k0^3 - (105*c^4)/(2*k0^2), (-1920*c^7)/k0^4 + ((1792*I)*c^6)/k0^3 + (576*c^5)/k0^2 - ((64*I)*c^4)/k0, (63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (-11*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, (143*(682591*c^12 - (1504800*I)*c^11*k0 - 1480380*c^10*k0^2 + (850500*I)*c^9*k0^3 + 312795*c^8*k0^4 - (75600*I)*c^7*k0^5 - 11760*c^6*k0^6 + (1080*I)*c^5*k0^7 + 45*c^4*k0^8))/(640*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-6 b/besseltransforms/4-4-6 new file mode 100644 index 0000000..9c77b74 --- /dev/null +++ b/besseltransforms/4-4-6 @@ -0,0 +1,2 @@ +((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1120*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(6720*k^6))/k0^4 +SeriesData[k, Infinity, {(6*c^4)/k0^4, (-105*c^5)/k0^4 + ((35*I)*c^4)/k0^3, (896*c^6)/k0^4 - ((576*I)*c^5)/k0^3 - (96*c^4)/k0^2, (-315*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 160*c^4 + (15888*c^8)/k0^4 - ((19200*I)*c^7)/k0^3 - (8960*c^6)/k0^2 + ((1920*I)*c^5)/k0, (-231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (143*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1] diff --git a/besseltransforms/4-4-7 b/besseltransforms/4-4-7 new file mode 100644 index 0000000..0ba1e1c --- /dev/null +++ b/besseltransforms/4-4-7 @@ -0,0 +1,2 @@ +((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(840*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(5040*k^7))/k0^4 +SeriesData[k, Infinity, {(7*c^4)/k0^4, (-48*(3*c^5 - I*c^4*k0))/k0^4, (105*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), (-320*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^4, (693*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), (-64*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/k0^4, (143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-13*(c - I*k0)^12)/3072 + (13*(2*c - I*k0)^12)/768 - (13*(3*c - I*k0)^12)/512 + (13*(4*c - I*k0)^12)/768 - (13*(5*c - I*k0)^12)/3072)/k0^4}, 2, 11, 1] diff --git a/besseltransforms/5-1-0 b/besseltransforms/5-1-0 new file mode 100644 index 0000000..f5c54c7 --- /dev/null +++ b/besseltransforms/5-1-0 @@ -0,0 +1,2 @@ +(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 5/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 10/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - 10/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 5/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - 1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0 +SeriesData[k, Infinity, {((-225*I)*c^5)/k + (1575*c^6)/(2*k*k0), 0, (-3675*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (19845*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/5-1-1 b/besseltransforms/5-1-1 new file mode 100644 index 0000000..e376b4c --- /dev/null +++ b/besseltransforms/5-1-1 @@ -0,0 +1,2 @@ +(-5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(k*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(45*c^5)/(k*k0), 0, (-525*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (11025*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-2 b/besseltransforms/5-1-2 new file mode 100644 index 0000000..eb4edb0 --- /dev/null +++ b/besseltransforms/5-1-2 @@ -0,0 +1,2 @@ +(-5*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 10*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (2*(5*c - I*k0))/k^2 + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2])) + 1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (2*(6*c - I*k0))/k^2 - (2*(6*c - I*k0))/(k^2*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((315*I)*c^5)/k - (2205*c^6)/(2*k*k0), 0, (4725*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (-24255*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/5-1-3 b/besseltransforms/5-1-3 new file mode 100644 index 0000000..b07afd3 --- /dev/null +++ b/besseltransforms/5-1-3 @@ -0,0 +1,2 @@ +((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(-105*c^5)/(k*k0), 0, (945*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-17325*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-4 b/besseltransforms/5-1-4 new file mode 100644 index 0000000..6567ab6 --- /dev/null +++ b/besseltransforms/5-1-4 @@ -0,0 +1,2 @@ +((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0 +SeriesData[k, Infinity, {((-945*I)*c^5)/k + (6615*c^6)/(2*k*k0), 0, (-10395*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/5-1-5 b/besseltransforms/5-1-5 new file mode 100644 index 0000000..52d673d --- /dev/null +++ b/besseltransforms/5-1-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(945*c^5)/(k*k0), 0, (-3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (45045*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-6 b/besseltransforms/5-1-6 new file mode 100644 index 0000000..6b35f98 --- /dev/null +++ b/besseltransforms/5-1-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0 +SeriesData[k, Infinity, {(3840*c^5)/(k*k0), ((10395*I)*c^5)/k - (72765*c^6)/(2*k*k0), 0, (45045*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (-135135*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-1-7 b/besseltransforms/5-1-7 new file mode 100644 index 0000000..2c7756e --- /dev/null +++ b/besseltransforms/5-1-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(10395*c^5)/(k*k0), ((46080*I)*c^5)/k - (161280*c^6)/(k*k0), (45045*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-225225*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1] diff --git a/besseltransforms/5-2-0 b/besseltransforms/5-2-0 new file mode 100644 index 0000000..6e741c5 --- /dev/null +++ b/besseltransforms/5-2-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-2-1 b/besseltransforms/5-2-1 new file mode 100644 index 0000000..888a040 --- /dev/null +++ b/besseltransforms/5-2-1 @@ -0,0 +1,2 @@ +((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/(k*k0^2) +SeriesData[k, Infinity, {(-315*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-11025*c^6)/4 + (99225*c^8)/(8*k0^2) - ((9975*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] diff --git a/besseltransforms/5-2-2 b/besseltransforms/5-2-2 new file mode 100644 index 0000000..cc4cb40 --- /dev/null +++ b/besseltransforms/5-2-2 @@ -0,0 +1,2 @@ +(-((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) + 5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^2*k0^2) +SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1995*c^7)/k0^2 - ((2205*I)/2*c^6)/k0, 0, (-1575*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-3 b/besseltransforms/5-2-3 new file mode 100644 index 0000000..ad65f50 --- /dev/null +++ b/besseltransforms/5-2-3 @@ -0,0 +1,2 @@ +(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^3*k0^2) +SeriesData[k, Infinity, {(735*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (19845*c^6)/4 - (178605*c^8)/(8*k0^2) + ((17955*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] diff --git a/besseltransforms/5-2-4 b/besseltransforms/5-2-4 new file mode 100644 index 0000000..85a0280 --- /dev/null +++ b/besseltransforms/5-2-4 @@ -0,0 +1,2 @@ +(-(k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 5*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 10*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 10*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 5*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*k0^2) +SeriesData[k, Infinity, {(105*c^5)/k0^2, 0, (945*c^5)/2 - (5985*c^7)/k0^2 + ((6615*I)/2*c^6)/k0, 0, (3465*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-5 b/besseltransforms/5-2-5 new file mode 100644 index 0000000..78e9161 --- /dev/null +++ b/besseltransforms/5-2-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/k^5 + (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(5*k^5))/k0^2 +SeriesData[k, Infinity, {(384*c^5)/k0^2, (-6615*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-72765*c^6)/4 + (654885*c^8)/(8*k0^2) - ((65835*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-6 b/besseltransforms/5-2-6 new file mode 100644 index 0000000..aa76553 --- /dev/null +++ b/besseltransforms/5-2-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(6*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(3*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(3*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(6*k^6))/k0^2 +SeriesData[k, Infinity, {(945*c^5)/k0^2, (-13440*c^6)/k0^2 + ((3840*I)*c^5)/k0, (-10395*c^5)/2 + (65835*c^7)/k0^2 - ((72765*I)/2*c^6)/k0, 0, (-15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-2-7 b/besseltransforms/5-2-7 new file mode 100644 index 0000000..8797403 --- /dev/null +++ b/besseltransforms/5-2-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(7*k^7) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/(7*k^7) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(7*k^7) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/(7*k^7) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(7*k^7))/k0^2 +SeriesData[k, Infinity, {(1920*c^5)/k0^2, (-72765*c^6)/(2*k0^2) + ((10395*I)*c^5)/k0, -23040*c^5 + (291840*c^7)/k0^2 - ((161280*I)*c^6)/k0, (945945*c^6)/4 - (8513505*c^8)/(8*k0^2) + ((855855*I)*c^7)/k0 - (45045*I)/2*c^5*k0, 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/5-3-0 b/besseltransforms/5-3-0 new file mode 100644 index 0000000..4795bb0 --- /dev/null +++ b/besseltransforms/5-3-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-3-1 b/besseltransforms/5-3-1 new file mode 100644 index 0000000..1c8226b --- /dev/null +++ b/besseltransforms/5-3-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-3-2 b/besseltransforms/5-3-2 new file mode 100644 index 0000000..39fc95b --- /dev/null +++ b/besseltransforms/5-3-2 @@ -0,0 +1,2 @@ +(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 5*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(6*k^2*k0^3) +SeriesData[k, Infinity, {(105*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/5-3-3 b/besseltransforms/5-3-3 new file mode 100644 index 0000000..cf02c58 --- /dev/null +++ b/besseltransforms/5-3-3 @@ -0,0 +1,2 @@ +((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(24*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(12*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(12*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(24*k^3))/k0^3 +SeriesData[k, Infinity, {(15*c^5)/k0^3, 0, (-35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (315*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-165*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-4 b/besseltransforms/5-3-4 new file mode 100644 index 0000000..a0ae761 --- /dev/null +++ b/besseltransforms/5-3-4 @@ -0,0 +1,2 @@ +((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(6*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(6*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(12*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(60*k^4))/k0^3 +SeriesData[k, Infinity, {(48*c^5)/k0^3, (-735*c^6)/(2*k0^3) + ((105*I)*c^5)/k0^2, 0, (315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (-693*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-5 b/besseltransforms/5-3-5 new file mode 100644 index 0000000..03014f2 --- /dev/null +++ b/besseltransforms/5-3-5 @@ -0,0 +1,2 @@ +((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(24*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(12*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(12*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(24*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(120*k^5))/k0^3 +SeriesData[k, Infinity, {(105*c^5)/k0^3, (-1344*c^6)/k0^3 + ((384*I)*c^5)/k0^2, (315*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (-1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (429*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-6 b/besseltransforms/5-3-6 new file mode 100644 index 0000000..abac3c1 --- /dev/null +++ b/besseltransforms/5-3-6 @@ -0,0 +1,2 @@ +((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(42*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(21*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(21*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(42*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(210*k^6))/k0^3 +SeriesData[k, Infinity, {(192*c^5)/k0^3, (-6615*c^6)/(2*k0^3) + ((945*I)*c^5)/k0^2, (24320*c^7)/k0^3 - ((13440*I)*c^6)/k0^2 - (1920*c^5)/k0, (-3465*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (3003*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-3-7 b/besseltransforms/5-3-7 new file mode 100644 index 0000000..6b8e845 --- /dev/null +++ b/besseltransforms/5-3-7 @@ -0,0 +1,2 @@ +((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8))/(336*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8))/(168*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(168*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(336*k^7))/k0^3 +SeriesData[k, Infinity, {(315*c^5)/k0^3, (-6720*c^6)/k0^3 + ((1920*I)*c^5)/k0^2, (3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), (-7680*I)*c^5 - (362880*c^8)/k0^3 + ((291840*I)*c^7)/k0^2 + (80640*c^6)/k0, (15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-2145*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1] diff --git a/besseltransforms/5-4-0 b/besseltransforms/5-4-0 new file mode 100644 index 0000000..0bee104 --- /dev/null +++ b/besseltransforms/5-4-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-4-1 b/besseltransforms/5-4-1 new file mode 100644 index 0000000..5307eb9 --- /dev/null +++ b/besseltransforms/5-4-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 2837835 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 4725 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 15 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 72765 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 105 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 3 E Sin[-- + k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------ + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + -------------------------------- does not converge on {0, Infinity}. + 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-4-2 b/besseltransforms/5-4-2 new file mode 100644 index 0000000..9e864cd --- /dev/null +++ b/besseltransforms/5-4-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) + 4 +Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-4-3 b/besseltransforms/5-4-3 new file mode 100644 index 0000000..a9c50ff --- /dev/null +++ b/besseltransforms/5-4-3 @@ -0,0 +1,2 @@ +((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(120*k^3))/k0^4 +SeriesData[k, Infinity, {(8*c^5)/k0^4, (-105*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (165*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-4 b/besseltransforms/5-4-4 new file mode 100644 index 0000000..5e9e365 --- /dev/null +++ b/besseltransforms/5-4-4 @@ -0,0 +1,2 @@ +((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(48*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(24*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(24*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(48*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(240*k^4))/k0^4 +SeriesData[k, Infinity, {(15*c^5)/k0^4, (-168*c^6)/k0^4 + ((48*I)*c^5)/k0^3, (35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), 0, (-105*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (33*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-5 b/besseltransforms/5-4-5 new file mode 100644 index 0000000..120e442 --- /dev/null +++ b/besseltransforms/5-4-5 @@ -0,0 +1,2 @@ +((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(168*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(84*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(84*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(168*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(840*k^5))/k0^4 +SeriesData[k, Infinity, {(24*c^5)/k0^4, (-735*c^6)/(2*k0^4) + ((105*I)*c^5)/k0^3, (2432*c^7)/k0^4 - ((1344*I)*c^6)/k0^3 - (192*c^5)/k0^2, (-315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (231*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (-429*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-6 b/besseltransforms/5-4-6 new file mode 100644 index 0000000..a9776fd --- /dev/null +++ b/besseltransforms/5-4-6 @@ -0,0 +1,2 @@ +((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1344*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(672*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(672*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(1344*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(6720*k^6))/k0^4 +SeriesData[k, Infinity, {(35*c^5)/k0^4, (-672*c^6)/k0^4 + ((192*I)*c^5)/k0^3, (315*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), (-30240*c^8)/k0^4 + ((24320*I)*c^7)/k0^3 + (6720*c^6)/k0^2 - ((640*I)*c^5)/k0, (1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (-143*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-4-7 b/besseltransforms/5-4-7 new file mode 100644 index 0000000..f0941eb --- /dev/null +++ b/besseltransforms/5-4-7 @@ -0,0 +1,2 @@ +((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1008*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(504*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(504*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(1008*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(5040*k^7))/k0^4 +SeriesData[k, Infinity, {(48*c^5)/k0^4, (-2205*c^6)/(2*k0^4) + ((315*I)*c^5)/k0^3, (12160*c^7)/k0^4 - ((6720*I)*c^6)/k0^3 - (960*c^5)/k0^2, (-3465*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 1920*c^5 + (347840*c^9)/k0^4 - ((362880*I)*c^8)/k0^3 - (145920*c^7)/k0^2 + ((26880*I)*c^6)/k0, (-3003*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (2145*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1] diff --git a/besseltransforms/5-5-0 b/besseltransforms/5-5-0 new file mode 100644 index 0000000..9d67bbd --- /dev/null +++ b/besseltransforms/5-5-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-1 b/besseltransforms/5-5-1 new file mode 100644 index 0000000..003ca0a --- /dev/null +++ b/besseltransforms/5-5-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 2837835 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 4725 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 15 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 72765 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 105 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 3 E Sin[-- + k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------ + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + -------------------------------- does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-2 b/besseltransforms/5-5-2 new file mode 100644 index 0000000..67d7ff3 --- /dev/null +++ b/besseltransforms/5-5-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 15 E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-3 b/besseltransforms/5-5-3 new file mode 100644 index 0000000..f8bcb24 --- /dev/null +++ b/besseltransforms/5-5-3 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 41247931725 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 11486475 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 11486475 E Cos[-- + k x] 45045 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 45045 E Cos[-- + k x] 945 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 945 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 218243025 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 218243025 E Sin[-- + k x] 405405 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 405405 E Sin[-- + k x] 3465 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 3465 E Sin[-- + k x] 35 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 35 E Sin[-- + k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ---------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/5-5-4 b/besseltransforms/5-5-4 new file mode 100644 index 0000000..6c06a03 --- /dev/null +++ b/besseltransforms/5-5-4 @@ -0,0 +1,2 @@ +((k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(1680*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(336*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(168*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(168*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(336*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(1680*k^4))/k0^5 +SeriesData[k, Infinity, {(4*c^5)/k0^5, (-105*c^6)/(2*k0^5) + ((15*I)*c^5)/k0^4, (304*c^7)/k0^5 - ((168*I)*c^6)/k0^4 - (24*c^5)/k0^3, (-35*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), 0, (21*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^5), 0, (-33*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/5-5-5 b/besseltransforms/5-5-5 new file mode 100644 index 0000000..385e34f --- /dev/null +++ b/besseltransforms/5-5-5 @@ -0,0 +1,2 @@ +((35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(13440*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(2688*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1344*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(1344*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(2688*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(13440*k^5))/k0^5 +SeriesData[k, Infinity, {(5*c^5)/k0^5, (-84*c^6)/k0^5 + ((24*I)*c^5)/k0^4, (35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-3024*c^8)/k0^5 + ((2432*I)*c^7)/k0^4 + (672*c^6)/k0^3 - ((64*I)*c^5)/k0^2, (105*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), 0, (-11*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (143*(443611*c^13 - (847392*I)*c^12*k0 - 721992*c^11*k0^2 + (358974*I)*c^10*k0^3 + 114135*c^9*k0^4 - (23814*I)*c^8*k0^5 - 3192*c^7*k0^6 + (252*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/5-5-6 b/besseltransforms/5-5-6 new file mode 100644 index 0000000..f599039 --- /dev/null +++ b/besseltransforms/5-5-6 @@ -0,0 +1,2 @@ +((k^8*(-315 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(60480*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(12096*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(6048*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(6048*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(12096*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(60480*k^6))/k0^5 +SeriesData[k, Infinity, {(6*c^5)/k0^5, (-245*c^6)/(2*k0^5) + ((35*I)*c^5)/k0^4, (1216*c^7)/k0^5 - ((672*I)*c^6)/k0^4 - (96*c^5)/k0^3, (-315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^5), (86960*c^9)/(3*k0^5) - ((30240*I)*c^8)/k0^4 - (12160*c^7)/k0^3 + ((2240*I)*c^6)/k0^2 + (160*c^5)/k0, (-231*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^5), 0, (143*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/5-5-7 b/besseltransforms/5-5-7 new file mode 100644 index 0000000..35af23d --- /dev/null +++ b/besseltransforms/5-5-7 @@ -0,0 +1,2 @@ +((21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(40320*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(8064*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(4032*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(4032*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(8064*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(40320*k^7))/k0^5 +SeriesData[k, Infinity, {(7*c^5)/k0^5, (-24*(7*c^6 - (2*I)*c^5*k0))/k0^5, (105*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-80*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/k0^5, (1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), (-32*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/k0^5, (143*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (-715*(443611*c^13 - (847392*I)*c^12*k0 - 721992*c^11*k0^2 + (358974*I)*c^10*k0^3 + 114135*c^9*k0^4 - (23814*I)*c^8*k0^5 - 3192*c^7*k0^6 + (252*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1] diff --git a/besseltransforms/6-1-0 b/besseltransforms/6-1-0 new file mode 100644 index 0000000..2caaed1 --- /dev/null +++ b/besseltransforms/6-1-0 @@ -0,0 +1,2 @@ +(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 6/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 15/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - 20/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 15/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - 6/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + 1/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)))/k0 +SeriesData[k, Infinity, {(-225*c^6)/(k*k0), 0, (11025*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (-59535*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-1-1 b/besseltransforms/6-1-1 new file mode 100644 index 0000000..72999b9 --- /dev/null +++ b/besseltransforms/6-1-1 @@ -0,0 +1,2 @@ +(2/k - 6*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 15*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 20*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 15*(k^(-1) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 6*(k^(-1) - 1/(k*Sqrt[1 + k^2/(6*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(k*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((-1575*I)*c^6)/k + (6300*c^7)/(k*k0), 0, (-33075*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/6-1-2 b/besseltransforms/6-1-2 new file mode 100644 index 0000000..8885d97 --- /dev/null +++ b/besseltransforms/6-1-2 @@ -0,0 +1,2 @@ +(-6*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 15*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 20*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 15*(1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (2*(5*c - I*k0))/k^2 + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 6*(1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) - (2*(6*c - I*k0))/k^2 + (2*(6*c - I*k0))/(k^2*Sqrt[1 + k^2/(6*c - I*k0)^2])) + 1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (2*(7*c - I*k0))/k^2 + (2*(7*c - I*k0))/(k^2*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(315*c^6)/(k*k0), 0, (-14175*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (72765*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-1-3 b/besseltransforms/6-1-3 new file mode 100644 index 0000000..1390128 --- /dev/null +++ b/besseltransforms/6-1-3 @@ -0,0 +1,2 @@ +((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (6*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (15*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (20*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (15*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (6*(k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((2835*I)*c^6)/k - (11340*c^7)/(k*k0), 0, (51975*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/6-1-4 b/besseltransforms/6-1-4 new file mode 100644 index 0000000..6a73d23 --- /dev/null +++ b/besseltransforms/6-1-4 @@ -0,0 +1,2 @@ +((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (15*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (20*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (15*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)))/k0 +SeriesData[k, Infinity, {(-945*c^6)/(k*k0), 0, (31185*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (-135135*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-1-5 b/besseltransforms/6-1-5 new file mode 100644 index 0000000..afd5f59 --- /dev/null +++ b/besseltransforms/6-1-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (6*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (15*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (20*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (15*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (6*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((-10395*I)*c^6)/k + (41580*c^7)/(k*k0), 0, (-135135*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/6-1-6 b/besseltransforms/6-1-6 new file mode 100644 index 0000000..76c8354 --- /dev/null +++ b/besseltransforms/6-1-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (15*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (20*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (15*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)))/k0 +SeriesData[k, Infinity, {(10395*c^6)/(k*k0), 0, (-135135*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (405405*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-1-7 b/besseltransforms/6-1-7 new file mode 100644 index 0000000..f7222a7 --- /dev/null +++ b/besseltransforms/6-1-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (6*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (15*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (20*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (15*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (6*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(46080*c^6)/(k*k0), ((135135*I)*c^6)/k - (540540*c^7)/(k*k0), 0, (675675*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 6, 11, 1] diff --git a/besseltransforms/6-2-0 b/besseltransforms/6-2-0 new file mode 100644 index 0000000..4a3dea6 --- /dev/null +++ b/besseltransforms/6-2-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-2-1 b/besseltransforms/6-2-1 new file mode 100644 index 0000000..a042203 --- /dev/null +++ b/besseltransforms/6-2-1 @@ -0,0 +1,2 @@ +((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 15*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 15*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 6*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + (-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0))/(k*k0^2) +SeriesData[k, Infinity, {(45*c^6)/k0^2, 0, (1575*c^6)/2 - (51975*c^8)/(4*k0^2) + ((6300*I)*c^7)/k0, 0, (-3274425*c^8)/8 + (20155905*c^10)/(16*k0^2) - ((1157625*I)*c^9)/k0 + (66150*I)*c^7*k0 + (33075*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-2-2 b/besseltransforms/6-2-2 new file mode 100644 index 0000000..dd9197e --- /dev/null +++ b/besseltransforms/6-2-2 @@ -0,0 +1,2 @@ +-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 15*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 15*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2)/(k^2*k0^2)) +SeriesData[k, Infinity, {(-1260*c^7)/k0^2 + ((315*I)*c^6)/k0, 0, -28350*c^7 + (165375*c^9)/k0^2 - ((467775*I)/4*c^8)/k0 + (4725*I)/2*c^6*k0}, 7, 11, 1] diff --git a/besseltransforms/6-2-3 b/besseltransforms/6-2-3 new file mode 100644 index 0000000..f51020a --- /dev/null +++ b/besseltransforms/6-2-3 @@ -0,0 +1,2 @@ +(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 6*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 15*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 60*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 20*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 15*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 60*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - 6*k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3)/(3*k^3*k0^2) +SeriesData[k, Infinity, {(-105*c^6)/k0^2, 0, (-2835*c^6)/2 + (93555*c^8)/(4*k0^2) - ((11340*I)*c^7)/k0, 0, (5145525*c^8)/8 - (31673565*c^10)/(16*k0^2) + ((1819125*I)*c^9)/k0 - (103950*I)*c^7*k0 - (51975*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-2-4 b/besseltransforms/6-2-4 new file mode 100644 index 0000000..17c1dae --- /dev/null +++ b/besseltransforms/6-2-4 @@ -0,0 +1,2 @@ +(1/2 - 6*(1/4 - ((-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4)/k^4) + 15*(1/4 - ((-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/k^4) - 20*(1/4 - ((-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/k^4) + 15*(1/4 - ((-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/k^4) - 6*(1/4 - ((-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/k^4) - ((-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/k^4 - ((-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/k^4)/k0^2 +SeriesData[k, Infinity, {(3780*c^7)/k0^2 - ((945*I)*c^6)/k0, 0, 62370*c^7 - (363825*c^9)/k0^2 + ((1029105*I)/4*c^8)/k0 - (10395*I)/2*c^6*k0}, 7, 11, 1] diff --git a/besseltransforms/6-2-5 b/besseltransforms/6-2-5 new file mode 100644 index 0000000..f92ff20 --- /dev/null +++ b/besseltransforms/6-2-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (6*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(5*k^5) + (3*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 - (4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (3*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/k^5 - (6*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(5*k^5) + (k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5)/(5*k^5))/k0^2 +SeriesData[k, Infinity, {(945*c^6)/k0^2, 0, (10395*c^6)/2 - (343035*c^8)/(4*k0^2) + ((41580*I)*c^7)/k0, 0, (-13378365*c^8)/8 + (82351269*c^10)/(16*k0^2) - ((4729725*I)*c^9)/k0 + (270270*I)*c^7*k0 + (135135*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-2-6 b/besseltransforms/6-2-6 new file mode 100644 index 0000000..3b96abb --- /dev/null +++ b/besseltransforms/6-2-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/k^6 + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(2*k^6) - (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(3*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(2*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/k^6 + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(6*k^6))/k0^2 +SeriesData[k, Infinity, {(3840*c^6)/k0^2, (-41580*c^7)/k0^2 + ((10395*I)*c^6)/k0, 0, -270270*c^7 + (1576575*c^9)/k0^2 - ((4459455*I)/4*c^8)/k0 + (45045*I)/2*c^6*k0}, 6, 11, 1] diff --git a/besseltransforms/6-2-7 b/besseltransforms/6-2-7 new file mode 100644 index 0000000..3231c56 --- /dev/null +++ b/besseltransforms/6-2-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (6*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(7*k^7) + (15*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/(7*k^7) - (20*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(7*k^7) + (15*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/(7*k^7) - (6*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7))/(7*k^7) + (k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(7*k^7))/k0^2 +SeriesData[k, Infinity, {(10395*c^6)/k0^2, (-184320*c^7)/k0^2 + ((46080*I)*c^6)/k0, (-135135*c^6)/2 + (4459455*c^8)/(4*k0^2) - ((540540*I)*c^7)/k0, 0, (66891825*c^8)/8 - (411756345*c^10)/(16*k0^2) + ((23648625*I)*c^9)/k0 - (1351350*I)*c^7*k0 - (675675*c^6*k0^2)/8}, 6, 11, 1] diff --git a/besseltransforms/6-3-0 b/besseltransforms/6-3-0 new file mode 100644 index 0000000..b942fa3 --- /dev/null +++ b/besseltransforms/6-3-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-3-1 b/besseltransforms/6-3-1 new file mode 100644 index 0000000..daed903 --- /dev/null +++ b/besseltransforms/6-3-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x c x 6 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-3-2 b/besseltransforms/6-3-2 new file mode 100644 index 0000000..ccb328f --- /dev/null +++ b/besseltransforms/6-3-2 @@ -0,0 +1,2 @@ +(-6*(((-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/(3*k^2)) + 15*(((-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2)) - 20*(((-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/(3*k^2)) + 15*(((-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^2)) - 6*(((-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^2)) + ((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/(3*k^2) + ((-3 + 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3)/(3*k^2))/k0^3 +SeriesData[k, Infinity, {(-15*c^6)/k0^3, 0, (315*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-9450*I)*c^7 - (2879415*c^10)/(16*k0^3) + ((165375*I)*c^9)/k0^2 + (467775*c^8)/(8*k0) - (4725*c^6*k0)/8}, 5, 11, 1] diff --git a/besseltransforms/6-3-3 b/besseltransforms/6-3-3 new file mode 100644 index 0000000..44cb237 --- /dev/null +++ b/besseltransforms/6-3-3 @@ -0,0 +1,2 @@ +((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4)/(4*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(8*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(6*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(8*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(4*k^3) + (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4)/(24*k^3))/k0^3 +SeriesData[k, Infinity, {(420*c^7)/k0^3 - ((105*I)*c^6)/k0^2, 0, (-945*I)/2*c^6 - (33075*c^9)/k0^3 + ((93555*I)/4*c^8)/k0^2 + (5670*c^7)/k0, 0, (10395*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/6-3-4 b/besseltransforms/6-3-4 new file mode 100644 index 0000000..63608ab --- /dev/null +++ b/besseltransforms/6-3-4 @@ -0,0 +1,2 @@ +((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(10*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(4*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(3*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(4*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(10*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5)/(60*k^4))/k0^3 +SeriesData[k, Infinity, {(105*c^6)/k0^3, 0, (-945*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (20790*I)*c^7 + (6334713*c^10)/(16*k0^3) - ((363825*I)*c^9)/k0^2 - (1029105*c^8)/(8*k0) + (10395*c^6*k0)/8}, 5, 11, 1] diff --git a/besseltransforms/6-3-5 b/besseltransforms/6-3-5 new file mode 100644 index 0000000..f14412a --- /dev/null +++ b/besseltransforms/6-3-5 @@ -0,0 +1,2 @@ +((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(20*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(8*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(6*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(8*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(20*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(120*k^5))/k0^3 +SeriesData[k, Infinity, {(384*c^6)/k0^3, (-3780*c^7)/k0^3 + ((945*I)*c^6)/k0^2, 0, (3465*I)/2*c^6 + (121275*c^9)/k0^3 - ((343035*I)/4*c^8)/k0^2 - (20790*c^7)/k0, 0, (-27027*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/6-3-6 b/besseltransforms/6-3-6 new file mode 100644 index 0000000..416d8ec --- /dev/null +++ b/besseltransforms/6-3-6 @@ -0,0 +1,2 @@ +((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(35*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(14*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(21*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(14*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(35*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(210*k^6))/k0^3 +SeriesData[k, Infinity, {(945*c^6)/k0^3, (-15360*c^7)/k0^3 + ((3840*I)*c^6)/k0^2, (10395*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-90090*I)*c^7 - (27450423*c^10)/(16*k0^3) + ((1576575*I)*c^9)/k0^2 + (4459455*c^8)/(8*k0) - (45045*c^6*k0)/8}, 5, 11, 1] diff --git a/besseltransforms/6-3-7 b/besseltransforms/6-3-7 new file mode 100644 index 0000000..3527f20 --- /dev/null +++ b/besseltransforms/6-3-7 @@ -0,0 +1,2 @@ +((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(56*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8))/(112*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(84*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(112*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(56*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(336*k^7))/k0^3 +SeriesData[k, Infinity, {(1920*c^6)/k0^3, (-41580*c^7)/k0^3 + ((10395*I)*c^6)/k0^2, (380160*c^8)/k0^3 - ((184320*I)*c^7)/k0^2 - (23040*c^6)/k0, (-45045*I)/2*c^6 - (1576575*c^9)/k0^3 + ((4459455*I)/4*c^8)/k0^2 + (270270*c^7)/k0, 0, (135135*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/6-4-0 b/besseltransforms/6-4-0 new file mode 100644 index 0000000..dbda98f --- /dev/null +++ b/besseltransforms/6-4-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-4-1 b/besseltransforms/6-4-1 new file mode 100644 index 0000000..d12b458 --- /dev/null +++ b/besseltransforms/6-4-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x c x 6 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-4-2 b/besseltransforms/6-4-2 new file mode 100644 index 0000000..9dea599 --- /dev/null +++ b/besseltransforms/6-4-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -21606059475 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 14189175 E Cos[-- - k x] 70945875 E Cos[-- - k x] 23648625 E Cos[-- - k x] 70945875 E Cos[-- - k x] 14189175 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 31185 E Cos[-- - k x] 155925 E Cos[-- - k x] 51975 E Cos[-- - k x] 155925 E Cos[-- - k x] 31185 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 315 E Cos[-- - k x] 1575 E Cos[-- - k x] 525 E Cos[-- - k x] 1575 E Cos[-- - k x] 315 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 310134825 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 516891375 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 310134825 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 405405 E Sin[-- - k x] 2027025 E Sin[-- - k x] 675675 E Sin[-- - k x] 2027025 E Sin[-- - k x] 405405 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 945 E Sin[-- - k x] 4725 E Sin[-- - k x] 1575 E Sin[-- - k x] 4725 E Sin[-- - k x] 945 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 45 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 45 E Sin[-- - k x] 15 E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------ + ---------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- - ---------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ---------------------------------------- + ------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + ------------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ---------------------------------- - ---------------------------------- - --------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. + 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 17/2 4 23/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 13/2 4 19/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 9/2 4 15/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 5/2 4 11/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 4 7/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 19/2 4 25/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 15/2 4 21/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 11/2 4 17/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 7/2 4 13/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 3/2 4 9/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-4-3 b/besseltransforms/6-4-3 new file mode 100644 index 0000000..d520464 --- /dev/null +++ b/besseltransforms/6-4-3 @@ -0,0 +1,2 @@ +((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(20*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(8*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(6*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(8*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(20*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5)/(120*k^3))/k0^4 +SeriesData[k, Infinity, {(15*c^6)/k0^4, 0, (-105*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^4), 0, (189*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^4), 0, (-165*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-4 b/besseltransforms/6-4-4 new file mode 100644 index 0000000..367e6eb --- /dev/null +++ b/besseltransforms/6-4-4 @@ -0,0 +1,2 @@ +((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(40*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(16*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(12*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(16*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(40*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6)/(240*k^4))/k0^4 +SeriesData[k, Infinity, {(48*c^6)/k0^4, (-420*c^7)/k0^4 + ((105*I)*c^6)/k0^3, 0, (315*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^4), 0, (-2079*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-5 b/besseltransforms/6-4-5 new file mode 100644 index 0000000..2b982d5 --- /dev/null +++ b/besseltransforms/6-4-5 @@ -0,0 +1,2 @@ +((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(140*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(56*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(42*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(56*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(140*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(840*k^5))/k0^4 +SeriesData[k, Infinity, {(105*c^6)/k0^4, (-1536*c^7)/k0^4 + ((384*I)*c^6)/k0^3, (945*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^4), 0, (-693*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^4), 0, (429*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-6 b/besseltransforms/6-4-6 new file mode 100644 index 0000000..ed31408 --- /dev/null +++ b/besseltransforms/6-4-6 @@ -0,0 +1,2 @@ +((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1120*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(448*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(336*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(448*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(1120*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(6720*k^6))/k0^4 +SeriesData[k, Infinity, {(192*c^6)/k0^4, (-3780*c^7)/k0^4 + ((945*I)*c^6)/k0^3, (31680*c^8)/k0^4 - ((15360*I)*c^7)/k0^3 - (1920*c^6)/k0^2, (-3465*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^4), 0, (9009*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-4-7 b/besseltransforms/6-4-7 new file mode 100644 index 0000000..f9a4830 --- /dev/null +++ b/besseltransforms/6-4-7 @@ -0,0 +1,2 @@ +((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(840*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(336*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(252*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(336*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(840*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(5040*k^7))/k0^4 +SeriesData[k, Infinity, {(315*c^6)/k0^4, (-7680*c^7)/k0^4 + ((1920*I)*c^6)/k0^3, (10395*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^4), (-537600*c^9)/k0^4 + ((380160*I)*c^8)/k0^3 + (92160*c^7)/k0^2 - ((7680*I)*c^6)/k0, (9009*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^4), 0, (-2145*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^4)}, 4, 11, 1] diff --git a/besseltransforms/6-5-0 b/besseltransforms/6-5-0 new file mode 100644 index 0000000..4116622 --- /dev/null +++ b/besseltransforms/6-5-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-1 b/besseltransforms/6-5-1 new file mode 100644 index 0000000..8e2366b --- /dev/null +++ b/besseltransforms/6-5-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x c x 6 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-2 b/besseltransforms/6-5-2 new file mode 100644 index 0000000..be33b7d --- /dev/null +++ b/besseltransforms/6-5-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -21606059475 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 324090892125 E Cos[-- - k x] 64818178425 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 4729725 E Cos[-- - k x] 14189175 E Cos[-- - k x] 70945875 E Cos[-- - k x] 23648625 E Cos[-- - k x] 70945875 E Cos[-- - k x] 14189175 E Cos[-- - k x] 4729725 E Cos[-- - k x] 10395 E Cos[-- - k x] 31185 E Cos[-- - k x] 155925 E Cos[-- - k x] 51975 E Cos[-- - k x] 155925 E Cos[-- - k x] 31185 E Cos[-- - k x] 10395 E Cos[-- - k x] 105 E Cos[-- - k x] 315 E Cos[-- - k x] 1575 E Cos[-- - k x] 525 E Cos[-- - k x] 1575 E Cos[-- - k x] 315 E Cos[-- - k x] 105 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 9830757061125 E Sin[-- - k x] 1966151412225 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 103378275 E Sin[-- - k x] 310134825 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 516891375 E Sin[-- - k x] 1550674125 E Sin[-- - k x] 310134825 E Sin[-- - k x] 103378275 E Sin[-- - k x] 135135 E Sin[-- - k x] 405405 E Sin[-- - k x] 2027025 E Sin[-- - k x] 675675 E Sin[-- - k x] 2027025 E Sin[-- - k x] 405405 E Sin[-- - k x] 135135 E Sin[-- - k x] 315 E Sin[-- - k x] 945 E Sin[-- - k x] 4725 E Sin[-- - k x] 1575 E Sin[-- - k x] 4725 E Sin[-- - k x] 945 E Sin[-- - k x] 315 E Sin[-- - k x] 15 E Sin[-- - k x] 45 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 45 E Sin[-- - k x] 15 E Sin[-- - k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------ - ------------------------------------ + ---------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- - ---------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ----------------------------------------- + ---------------------------------------- - ---------------------------------------- + ------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + -------------------------------------- - ------------------------------------- + ------------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ---------------------------------- - ---------------------------------- - --------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-3 b/besseltransforms/6-5-3 new file mode 100644 index 0000000..47f6455 --- /dev/null +++ b/besseltransforms/6-5-3 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + -41247931725 E Cos[-- + k x] 123743795175 E Cos[-- + k x] 618718975875 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 618718975875 E Cos[-- + k x] 123743795175 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 11486475 E Cos[-- + k x] 34459425 E Cos[-- + k x] 172297125 E Cos[-- + k x] 57432375 E Cos[-- + k x] 172297125 E Cos[-- + k x] 34459425 E Cos[-- + k x] 11486475 E Cos[-- + k x] 45045 E Cos[-- + k x] 135135 E Cos[-- + k x] 675675 E Cos[-- + k x] 225225 E Cos[-- + k x] 675675 E Cos[-- + k x] 135135 E Cos[-- + k x] 45045 E Cos[-- + k x] 945 E Cos[-- + k x] 2835 E Cos[-- + k x] 14175 E Cos[-- + k x] 4725 E Cos[-- + k x] 14175 E Cos[-- + k x] 2835 E Cos[-- + k x] 945 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 6 E Sqrt[--] Cos[-- + k x] 15 E Sqrt[--] Cos[-- + k x] 20 E Sqrt[--] Cos[-- + k x] 15 E Sqrt[--] Cos[-- + k x] 6 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 3478575575475 E Sin[-- + k x] 17392877877375 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 17392877877375 E Sin[-- + k x] 3478575575475 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 218243025 E Sin[-- + k x] 654729075 E Sin[-- + k x] 3273645375 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 3273645375 E Sin[-- + k x] 654729075 E Sin[-- + k x] 218243025 E Sin[-- + k x] 405405 E Sin[-- + k x] 1216215 E Sin[-- + k x] 6081075 E Sin[-- + k x] 2027025 E Sin[-- + k x] 6081075 E Sin[-- + k x] 1216215 E Sin[-- + k x] 405405 E Sin[-- + k x] 3465 E Sin[-- + k x] 10395 E Sin[-- + k x] 51975 E Sin[-- + k x] 17325 E Sin[-- + k x] 51975 E Sin[-- + k x] 10395 E Sin[-- + k x] 3465 E Sin[-- + k x] 35 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 175 E Sin[-- + k x] 525 E Sin[-- + k x] 105 E Sin[-- + k x] 35 E Sin[-- + k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ + --------------------------------------- - --------------------------------------- + ---------------------------------------- - --------------------------------------- + ---------------------------------------- - --------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - ---------------------------------- + ----------------------------------- - ------------------------------------ + ----------------------------------- - ------------------------------------ + ----------------------------------- - ---------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - -------------------------------------------- + -------------------------------------------- - --------------------------------------------- + -------------------------------------------- - --------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ---------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ---------------------------------------- + ---------------------------------------- - ------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}. + 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 9/2 5 17/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5/2 5 13/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 5 9/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 19/2 5 27/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 15/2 5 23/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 11/2 5 19/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 7/2 5 15/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 3/2 5 11/2 + 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/6-5-4 b/besseltransforms/6-5-4 new file mode 100644 index 0000000..b475d54 --- /dev/null +++ b/besseltransforms/6-5-4 @@ -0,0 +1,2 @@ +((k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(1680*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(280*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(112*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(84*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(112*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(280*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(1680*k^4))/k0^5 +SeriesData[k, Infinity, {(15*c^6)/k0^5, (-192*c^7)/k0^5 + ((48*I)*c^6)/k0^4, (105*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^5), 0, (-63*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^5), 0, (33*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/6-5-5 b/besseltransforms/6-5-5 new file mode 100644 index 0000000..033cb55 --- /dev/null +++ b/besseltransforms/6-5-5 @@ -0,0 +1,2 @@ +((35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(13440*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(2240*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(896*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(672*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(896*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(2240*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(13440*k^5))/k0^5 +SeriesData[k, Infinity, {(24*c^6)/k0^5, (-420*c^7)/k0^5 + ((105*I)*c^6)/k0^4, (3168*c^8)/k0^5 - ((1536*I)*c^7)/k0^4 - (192*c^6)/k0^3, (-315*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^5), 0, (693*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^5), 0, (-429*(172480*c^13 - (259792*I)*c^12*k0 - 171108*c^11*k0^2 + (63987*I)*c^10*k0^3 + 14700*c^9*k0^4 - (2079*I)*c^8*k0^5 - 168*c^7*k0^6 + (6*I)*c^6*k0^7))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/6-5-6 b/besseltransforms/6-5-6 new file mode 100644 index 0000000..8a55259 --- /dev/null +++ b/besseltransforms/6-5-6 @@ -0,0 +1,2 @@ +((k^8*(-315 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(60480*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(10080*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(4032*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(3024*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(4032*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(10080*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(60480*k^6))/k0^5 +SeriesData[k, Infinity, {(35*c^6)/k0^5, (-768*c^7)/k0^5 + ((192*I)*c^6)/k0^4, (945*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^5), (-44800*c^9)/k0^5 + ((31680*I)*c^8)/k0^4 + (7680*c^7)/k0^3 - ((640*I)*c^6)/k0^2, (693*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^5), 0, (-143*(259792*c^12 - (342216*I)*c^11*k0 - 191961*c^10*k0^2 + (58800*I)*c^9*k0^3 + 10395*c^8*k0^4 - (1008*I)*c^7*k0^5 - 42*c^6*k0^6))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/6-5-7 b/besseltransforms/6-5-7 new file mode 100644 index 0000000..2f390fa --- /dev/null +++ b/besseltransforms/6-5-7 @@ -0,0 +1,2 @@ +((21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(40320*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(6720*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(2688*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(2016*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(2688*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(6720*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10)/(40320*k^7))/k0^5 +SeriesData[k, Infinity, {(48*c^6)/k0^5, (-1260*c^7)/k0^5 + ((315*I)*c^6)/k0^4, (15840*c^8)/k0^5 - ((7680*I)*c^7)/k0^4 - (960*c^6)/k0^3, (-3465*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^5), (585024*c^10)/k0^5 - ((537600*I)*c^9)/k0^4 - (190080*c^8)/k0^3 + ((30720*I)*c^7)/k0^2 + (1920*c^6)/k0, (-9009*(2716*c^11 - (3047*I)*c^10*k0 - 1400*c^9*k0^2 + (330*I)*c^8*k0^3 + 40*c^7*k0^4 - (2*I)*c^6*k0^5))/(16*k0^5), 0, (2145*(172480*c^13 - (259792*I)*c^12*k0 - 171108*c^11*k0^2 + (63987*I)*c^10*k0^3 + 14700*c^9*k0^4 - (2079*I)*c^8*k0^5 - 168*c^7*k0^6 + (6*I)*c^6*k0^7))/(32*k0^5)}, 3, 11, 1] diff --git a/besseltransforms/7-1-0 b/besseltransforms/7-1-0 new file mode 100644 index 0000000..83e622d --- /dev/null +++ b/besseltransforms/7-1-0 @@ -0,0 +1,2 @@ +(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 7/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 21/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - 35/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 35/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - 21/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + 7/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - 1/(Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)))/k0 +SeriesData[k, Infinity, {((11025*I)*c^7)/k - (99225*c^8)/(2*k*k0), 0, (297675*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1] diff --git a/besseltransforms/7-1-1 b/besseltransforms/7-1-1 new file mode 100644 index 0000000..619fe49 --- /dev/null +++ b/besseltransforms/7-1-1 @@ -0,0 +1,2 @@ +(-7*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 21*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 35*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 35*(k^(-1) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 21*(k^(-1) - 1/(k*Sqrt[1 + k^2/(6*c - I*k0)^2])) + 7*(k^(-1) - 1/(k*Sqrt[1 + k^2/(7*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(k*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(-1575*c^7)/(k*k0), 0, (33075*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-1-2 b/besseltransforms/7-1-2 new file mode 100644 index 0000000..a4632ba --- /dev/null +++ b/besseltransforms/7-1-2 @@ -0,0 +1,2 @@ +(-7*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 21*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 35*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 35*(1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (2*(5*c - I*k0))/k^2 + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 21*(1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) - (2*(6*c - I*k0))/k^2 + (2*(6*c - I*k0))/(k^2*Sqrt[1 + k^2/(6*c - I*k0)^2])) + 7*(1/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (2*(7*c - I*k0))/k^2 + (2*(7*c - I*k0))/(k^2*Sqrt[1 + k^2/(7*c - I*k0)^2])) + 1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)) + (2*(8*c - I*k0))/k^2 - (2*(8*c - I*k0))/(k^2*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {((-14175*I)*c^7)/k + (127575*c^8)/(2*k*k0), 0, (-363825*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1] diff --git a/besseltransforms/7-1-3 b/besseltransforms/7-1-3 new file mode 100644 index 0000000..f4c5a4c --- /dev/null +++ b/besseltransforms/7-1-3 @@ -0,0 +1,2 @@ +((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (7*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (21*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (35*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (35*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (21*(k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (7*(k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(7*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(2835*c^7)/(k*k0), 0, (-51975*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-1-4 b/besseltransforms/7-1-4 new file mode 100644 index 0000000..123b36b --- /dev/null +++ b/besseltransforms/7-1-4 @@ -0,0 +1,2 @@ +((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (7*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (21*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (35*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (35*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (21*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (7*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)))/k0 +SeriesData[k, Infinity, {((31185*I)*c^7)/k - (280665*c^8)/(2*k*k0), 0, (675675*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1] diff --git a/besseltransforms/7-1-5 b/besseltransforms/7-1-5 new file mode 100644 index 0000000..4ff1e02 --- /dev/null +++ b/besseltransforms/7-1-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (7*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (21*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (35*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (35*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (21*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (7*(k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(7*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(8*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(-10395*c^7)/(k*k0), 0, (135135*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-1-6 b/besseltransforms/7-1-6 new file mode 100644 index 0000000..b5b3a5e --- /dev/null +++ b/besseltransforms/7-1-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (21*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (21*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)))/k0 +SeriesData[k, Infinity, {((-135135*I)*c^7)/k + (1216215*c^8)/(2*k*k0), 0, (-2027025*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1] diff --git a/besseltransforms/7-1-7 b/besseltransforms/7-1-7 new file mode 100644 index 0000000..003aedb --- /dev/null +++ b/besseltransforms/7-1-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (7*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (21*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (35*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (35*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (21*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]) + (7*(k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(7*c - I*k0)^2]) - (k^6*(-7 + Sqrt[1 + k^2/(8*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0 +SeriesData[k, Infinity, {(135135*c^7)/(k*k0), 0, (-675675*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1] diff --git a/besseltransforms/7-2-0 b/besseltransforms/7-2-0 new file mode 100644 index 0000000..d8314d1 --- /dev/null +++ b/besseltransforms/7-2-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 2 21/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-2-1 b/besseltransforms/7-2-1 new file mode 100644 index 0000000..3ba0bd1 --- /dev/null +++ b/besseltransforms/7-2-1 @@ -0,0 +1,2 @@ +((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 7*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 21*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 35*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 35*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 21*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 7*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) - (-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0))/(k*k0^2) +SeriesData[k, Infinity, {(14175*c^8)/(2*k0^2) - ((1575*I)*c^7)/k0, 0, (-33075*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1] diff --git a/besseltransforms/7-2-2 b/besseltransforms/7-2-2 new file mode 100644 index 0000000..743a6ce --- /dev/null +++ b/besseltransforms/7-2-2 @@ -0,0 +1,2 @@ +(-((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) + 7*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 21*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 35*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 35*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 21*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 7*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2)/(k^2*k0^2) +SeriesData[k, Infinity, {(315*c^7)/k0^2, 0, (-4725*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-2-3 b/besseltransforms/7-2-3 new file mode 100644 index 0000000..a23033b --- /dev/null +++ b/besseltransforms/7-2-3 @@ -0,0 +1,2 @@ +(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 7*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 28*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 21*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 84*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 35*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 140*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 35*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 140*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - 21*k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 84*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 7*k^2*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 28*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 - k^2*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3)/(3*k^3*k0^2) +SeriesData[k, Infinity, {(-25515*c^8)/(2*k0^2) + ((2835*I)*c^7)/k0, 0, (51975*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1] diff --git a/besseltransforms/7-2-4 b/besseltransforms/7-2-4 new file mode 100644 index 0000000..8f2cb62 --- /dev/null +++ b/besseltransforms/7-2-4 @@ -0,0 +1,2 @@ +(-(k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 7*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 14*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 21*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 42*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 35*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 35*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 70*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 21*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 42*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 7*k^2*(-2 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 14*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(k^4*k0^2) +SeriesData[k, Infinity, {(-945*c^7)/k0^2, 0, (10395*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-2-5 b/besseltransforms/7-2-5 new file mode 100644 index 0000000..b995fe1 --- /dev/null +++ b/besseltransforms/7-2-5 @@ -0,0 +1,2 @@ +((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (7*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(5*k^5) + (21*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/(5*k^5) - (7*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (7*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/k^5 - (21*(k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(5*k^5) + (7*(k^4*(-5 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5))/(5*k^5) - (k^4*(-5 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5)/(5*k^5))/k0^2 +SeriesData[k, Infinity, {(93555*c^8)/(2*k0^2) - ((10395*I)*c^7)/k0, 0, (-135135*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1] diff --git a/besseltransforms/7-2-6 b/besseltransforms/7-2-6 new file mode 100644 index 0000000..2c3c7f5 --- /dev/null +++ b/besseltransforms/7-2-6 @@ -0,0 +1,2 @@ +((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(6*k^6) + (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(2*k^6) - (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(6*k^6) + (35*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(6*k^6) - (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(2*k^6) + (7*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(6*k^6))/k0^2 +SeriesData[k, Infinity, {(10395*c^7)/k0^2, 0, (-45045*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-2-7 b/besseltransforms/7-2-7 new file mode 100644 index 0000000..08204f7 --- /dev/null +++ b/besseltransforms/7-2-7 @@ -0,0 +1,2 @@ +((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/k^7 + (3*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/k^7 - (5*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/k^7 + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/k^7 - (3*(k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7))/k^7 + (k^6*(-7 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/k^7 - (k^6*(-7 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(7*k^7))/k0^2 +SeriesData[k, Infinity, {(46080*c^7)/k0^2, (-1216215*c^8)/(2*k0^2) + ((135135*I)*c^7)/k0, 0, (675675*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-3-0 b/besseltransforms/7-3-0 new file mode 100644 index 0000000..854eabc --- /dev/null +++ b/besseltransforms/7-3-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-3-1 b/besseltransforms/7-3-1 new file mode 100644 index 0000000..54b7244 --- /dev/null +++ b/besseltransforms/7-3-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-3-2 b/besseltransforms/7-3-2 new file mode 100644 index 0000000..74b61aa --- /dev/null +++ b/besseltransforms/7-3-2 @@ -0,0 +1,2 @@ +(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 7*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 14*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 21*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 42*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 35*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 35*k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 70*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 21*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 42*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 7*k^2*(-3 + 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 14*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3)/(6*k^2*k0^3) +SeriesData[k, Infinity, {(-2835*c^8)/(2*k0^3) + ((315*I)*c^7)/k0^2, 0, (4725*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1] diff --git a/besseltransforms/7-3-3 b/besseltransforms/7-3-3 new file mode 100644 index 0000000..00bb32f --- /dev/null +++ b/besseltransforms/7-3-3 @@ -0,0 +1,2 @@ +((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(24*k^3) + (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(8*k^3) - (35*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(24*k^3) + (35*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(24*k^3) - (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4))/(8*k^3) + (7*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4)/(24*k^3))/k0^3 +SeriesData[k, Infinity, {(-105*c^7)/k0^3, 0, (945*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^3), 0, (-10395*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-3-4 b/besseltransforms/7-3-4 new file mode 100644 index 0000000..1713d3f --- /dev/null +++ b/besseltransforms/7-3-4 @@ -0,0 +1,2 @@ +((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(60*k^4) + (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/(20*k^4) - (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/(12*k^4) + (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/(12*k^4) - (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(20*k^4) + (7*(k^4*(-15 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5))/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5)/(60*k^4))/k0^3 +SeriesData[k, Infinity, {(8505*c^8)/(2*k0^3) - ((945*I)*c^7)/k0^2, 0, (-10395*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1] diff --git a/besseltransforms/7-3-5 b/besseltransforms/7-3-5 new file mode 100644 index 0000000..65b066a --- /dev/null +++ b/besseltransforms/7-3-5 @@ -0,0 +1,2 @@ +((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(120*k^5) + (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(40*k^5) - (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(24*k^5) + (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(24*k^5) - (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(40*k^5) + (7*(5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(120*k^5))/k0^3 +SeriesData[k, Infinity, {(945*c^7)/k0^3, 0, (-3465*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^3), 0, (27027*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-3-6 b/besseltransforms/7-3-6 new file mode 100644 index 0000000..4ec742d --- /dev/null +++ b/besseltransforms/7-3-6 @@ -0,0 +1,2 @@ +((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(30*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(10*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(6*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(6*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(10*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(30*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(210*k^6))/k0^3 +SeriesData[k, Infinity, {(3840*c^7)/k0^3, (-93555*c^8)/(2*k0^3) + ((10395*I)*c^7)/k0^2, 0, (45045*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-3-7 b/besseltransforms/7-3-7 new file mode 100644 index 0000000..8d6266f --- /dev/null +++ b/besseltransforms/7-3-7 @@ -0,0 +1,2 @@ +((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(48*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(16*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(48*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(48*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(16*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(48*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8)/(336*k^7))/k0^3 +SeriesData[k, Infinity, {(10395*c^7)/k0^3, (-207360*c^8)/k0^3 + ((46080*I)*c^7)/k0^2, (45045*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^3), 0, (-135135*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^3)}, 6, 11, 1] diff --git a/besseltransforms/7-4-0 b/besseltransforms/7-4-0 new file mode 100644 index 0000000..38b67d7 --- /dev/null +++ b/besseltransforms/7-4-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-4-1 b/besseltransforms/7-4-1 new file mode 100644 index 0000000..e1c52ce --- /dev/null +++ b/besseltransforms/7-4-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-4-2 b/besseltransforms/7-4-2 new file mode 100644 index 0000000..58d2f5c --- /dev/null +++ b/besseltransforms/7-4-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) + 4 +Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-4-3 b/besseltransforms/7-4-3 new file mode 100644 index 0000000..55566eb --- /dev/null +++ b/besseltransforms/7-4-3 @@ -0,0 +1,2 @@ +((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5))/(120*k^3) + (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/(40*k^3) - (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/(24*k^3) + (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5))/(24*k^3) - (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5))/(40*k^3) + (7*(k^4*(-15 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5))/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5)/(120*k^3))/k0^4 +SeriesData[k, Infinity, {(945*c^8)/(2*k0^4) - ((105*I)*c^7)/k0^3, 0, (-945*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^4), 0, (3465*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^4)}, 6, 11, 1] diff --git a/besseltransforms/7-4-4 b/besseltransforms/7-4-4 new file mode 100644 index 0000000..89e1c6c --- /dev/null +++ b/besseltransforms/7-4-4 @@ -0,0 +1,2 @@ +((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(240*k^4) + (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(80*k^4) - (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(48*k^4) + (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(48*k^4) - (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6))/(80*k^4) + (7*(5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6))/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6)/(240*k^4))/k0^4 +SeriesData[k, Infinity, {(105*c^7)/k0^4, 0, (-315*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^4), 0, (2079*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-4-5 b/besseltransforms/7-4-5 new file mode 100644 index 0000000..090ee13 --- /dev/null +++ b/besseltransforms/7-4-5 @@ -0,0 +1,2 @@ +((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(120*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(40*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(24*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(24*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(40*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(120*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(840*k^5))/k0^4 +SeriesData[k, Infinity, {(384*c^7)/k0^4, (-8505*c^8)/(2*k0^4) + ((945*I)*c^7)/k0^3, 0, (3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^4), 0, (-9009*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-4-6 b/besseltransforms/7-4-6 new file mode 100644 index 0000000..c8a5a4d --- /dev/null +++ b/besseltransforms/7-4-6 @@ -0,0 +1,2 @@ +((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(960*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(320*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(192*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(192*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(320*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(960*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8)/(6720*k^6))/k0^4 +SeriesData[k, Infinity, {(945*c^7)/k0^4, (-17280*c^8)/k0^4 + ((3840*I)*c^7)/k0^3, (3465*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^4), 0, (-9009*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-4-7 b/besseltransforms/7-4-7 new file mode 100644 index 0000000..569ec89 --- /dev/null +++ b/besseltransforms/7-4-7 @@ -0,0 +1,2 @@ +((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(720*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(240*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(144*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(144*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(240*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(720*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(5040*k^7))/k0^4 +SeriesData[k, Infinity, {(1920*c^7)/k0^4, (-93555*c^8)/(2*k0^4) + ((10395*I)*c^7)/k0^3, (480000*c^9)/k0^4 - ((207360*I)*c^8)/k0^3 - (23040*c^7)/k0^2, (-45045*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^4), 0, (45045*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^4)}, 5, 11, 1] diff --git a/besseltransforms/7-5-0 b/besseltransforms/7-5-0 new file mode 100644 index 0000000..e69de29 diff --git a/besseltransforms/7-5-1 b/besseltransforms/7-5-1 new file mode 100644 index 0000000..a0de589 --- /dev/null +++ b/besseltransforms/7-5-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-5-2 b/besseltransforms/7-5-2 new file mode 100644 index 0000000..1b22dae --- /dev/null +++ b/besseltransforms/7-5-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) + 4 +Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-5-3 b/besseltransforms/7-5-3 new file mode 100644 index 0000000..772d6de --- /dev/null +++ b/besseltransforms/7-5-3 @@ -0,0 +1,10 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + 2 2 4 4 6 6 8 8 + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) + E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------) + 4 Sqrt[2] +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-5-4 b/besseltransforms/7-5-4 new file mode 100644 index 0000000..b8b1107 --- /dev/null +++ b/besseltransforms/7-5-4 @@ -0,0 +1,2 @@ +((k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(1680*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(240*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(80*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(48*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(48*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(80*k^4) + (k^6*(-35 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7)/(240*k^4) - (k^6*(-35 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 16*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7)/(1680*k^4))/k0^5 +SeriesData[k, Infinity, {(48*c^7)/k0^5, (-945*c^8)/(2*k0^5) + ((105*I)*c^7)/k0^4, 0, (315*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^5), 0, (-693*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-5-5 b/besseltransforms/7-5-5 new file mode 100644 index 0000000..997dca6 --- /dev/null +++ b/besseltransforms/7-5-5 @@ -0,0 +1,2 @@ +((35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(13440*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1920*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(640*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(384*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(384*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(640*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8)/(1920*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8)/(13440*k^5))/k0^5 +SeriesData[k, Infinity, {(105*c^7)/k0^5, (-1728*c^8)/k0^5 + ((384*I)*c^7)/k0^4, (315*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^5), 0, (-693*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^5), 0, (3003*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-5-6 b/besseltransforms/7-5-6 new file mode 100644 index 0000000..676c848 --- /dev/null +++ b/besseltransforms/7-5-6 @@ -0,0 +1,2 @@ +((k^8*(-315 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(60480*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(8640*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(2880*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(1728*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(1728*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(2880*k^6) + (k^8*(-315 + 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(8640*k^6) - (k^8*(-315 + 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 16*k^6*(-105 + 52*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 48*k^4*(-63 + 44*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*k^2*(-36 + 31*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(60480*k^6))/k0^5 +SeriesData[k, Infinity, {(192*c^7)/k0^5, (-8505*c^8)/(2*k0^5) + ((945*I)*c^7)/k0^4, (40000*c^9)/k0^5 - ((17280*I)*c^8)/k0^4 - (1920*c^7)/k0^3, (-3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^5), 0, (3003*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-5-7 b/besseltransforms/7-5-7 new file mode 100644 index 0000000..fd58f5a --- /dev/null +++ b/besseltransforms/7-5-7 @@ -0,0 +1,2 @@ +((21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(40320*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(5760*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(1920*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(1152*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(1152*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(1920*k^7) + (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10)/(5760*k^7) - (21*k^10 + 4*k^8*(105 - 32*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 112*k^6*(15 - 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 384*k^4*(7 - 5*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 + 128*k^2*(15 - 13*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8 - 512*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^10)/(40320*k^7))/k0^5 +SeriesData[k, Infinity, {(315*c^7)/k0^5, (-8640*c^8)/k0^5 + ((1920*I)*c^7)/k0^4, (3465*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^5), (-760320*c^10)/k0^5 + ((480000*I)*c^9)/k0^4 + (103680*c^8)/k0^3 - ((7680*I)*c^7)/k0^2, (9009*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^5), 0, (-15015*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^5)}, 4, 11, 1] diff --git a/besseltransforms/7-6-0 b/besseltransforms/7-6-0 new file mode 100644 index 0000000..200acc1 --- /dev/null +++ b/besseltransforms/7-6-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 0 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 6 29/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 0 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-1 b/besseltransforms/7-6-1 new file mode 100644 index 0000000..f11cdca --- /dev/null +++ b/besseltransforms/7-6-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 1 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 6 29/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 1 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-2 b/besseltransforms/7-6-2 new file mode 100644 index 0000000..2dcbcd8 --- /dev/null +++ b/besseltransforms/7-6-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 2 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) + 4 +Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 6 29/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 2 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-3 b/besseltransforms/7-6-3 new file mode 100644 index 0000000..72779e9 --- /dev/null +++ b/besseltransforms/7-6-3 @@ -0,0 +1,10 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 3 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + 2 2 4 4 6 6 8 8 + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) + E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------) + 4 Sqrt[2] +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 6 29/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 3 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-4 b/besseltransforms/7-6-4 new file mode 100644 index 0000000..4d79144 --- /dev/null +++ b/besseltransforms/7-6-4 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 4 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) (63 (-41829913125 + 5320972800 k x - 2389770240 k x - 11995709440 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (105411381075 - 22348085760 k x + 44281036800 k x - 58133053440 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 6 29/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^6*x^5), {x, 0, Infinity}, Assumptions -> n == 4 && q == 6 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-6-5 b/besseltransforms/7-6-5 new file mode 100644 index 0000000..04e35d5 --- /dev/null +++ b/besseltransforms/7-6-5 @@ -0,0 +1,2 @@ +((k^8*(-315 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(120960*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(17280*k^5) + (k^8*(-315 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(5760*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(3456*k^5) + (k^8*(-315 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(3456*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(5760*k^5) + (k^8*(-315 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9)/(17280*k^5) - (k^8*(-315 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 8*k^6*(-105 + 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 48*k^4*(-21 + 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 64*k^2*(-9 + 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9)/(120960*k^5))/k0^6 +SeriesData[k, Infinity, {(24*c^7)/k0^6, (-945*c^8)/(2*k0^6) + ((105*I)*c^7)/k0^5, (4000*c^9)/k0^6 - ((1728*I)*c^8)/k0^5 - (192*c^7)/k0^4, (-315*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^6), 0, (231*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^6), 0, (-429*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^6)}, 3, 11, 1] diff --git a/besseltransforms/7-6-6 b/besseltransforms/7-6-6 new file mode 100644 index 0000000..80f7f8d --- /dev/null +++ b/besseltransforms/7-6-6 @@ -0,0 +1,2 @@ +((63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10)/(241920*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10)/(34560*k^6) + (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10)/(11520*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10)/(6912*k^6) + (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10)/(6912*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10)/(11520*k^6) + (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10)/(34560*k^6) - (63*k^10 + 2*k^8*(315 - 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 16*k^6*(105 - 64*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 96*k^4*(21 - 16*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 + 128*k^2*(9 - 8*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8 - 256*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^10)/(241920*k^6))/k0^6 +SeriesData[k, Infinity, {(35*c^7)/k0^6, (-864*c^8)/k0^6 + ((192*I)*c^7)/k0^5, (315*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^6), (-63360*c^10)/k0^6 + ((40000*I)*c^9)/k0^5 + (8640*c^8)/k0^4 - ((640*I)*c^7)/k0^3, (693*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^6), 0, (-1001*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^6)}, 3, 11, 1] diff --git a/besseltransforms/7-6-7 b/besseltransforms/7-6-7 new file mode 100644 index 0000000..d9750be --- /dev/null +++ b/besseltransforms/7-6-7 @@ -0,0 +1,2 @@ +((k^10*(-693 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^11)/(1330560*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^11)/(190080*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^11)/(63360*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^11)/(38016*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^11)/(38016*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^11)/(63360*k^7) + (k^10*(-693 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^11)/(190080*k^7) - (k^10*(-693 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 4*k^8*(-1155 + 512*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 144*k^6*(-77 + 48*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 128*k^4*(-99 + 76*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*k^2*(-55 + 49*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9 + 1536*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^11)/(1330560*k^7))/k0^6 +SeriesData[k, Infinity, {(48*c^7)/k0^6, (-2835*c^8)/(2*k0^6) + ((315*I)*c^7)/k0^5, (20000*c^9)/k0^6 - ((8640*I)*c^8)/k0^5 - (960*c^7)/k0^4, (-3465*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^6), (925248*c^11)/k0^6 - ((760320*I)*c^10)/k0^5 - (240000*c^9)/k0^4 + ((34560*I)*c^8)/k0^3 + (1920*c^7)/k0^2, (-3003*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^6), 0, (2145*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^6)}, 3, 11, 1] diff --git a/besseltransforms/7-7-0 b/besseltransforms/7-7-0 new file mode 100644 index 0000000..78ce17e --- /dev/null +++ b/besseltransforms/7-7-0 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 0 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 7 31/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 0 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-1 b/besseltransforms/7-7-1 new file mode 100644 index 0000000..94b1305 --- /dev/null +++ b/besseltransforms/7-7-1 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 1 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi + -(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x])) + 4 4 +Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}. + 19/2 7 31/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 1 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-2 b/besseltransforms/7-7-2 new file mode 100644 index 0000000..0f84d8c --- /dev/null +++ b/besseltransforms/7-7-2 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 2 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + -(E (-1 + E ) (15 (-43692253605 + 3528645120 k x - 590413824 k x + 352321536 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k x + 681246720 k x - 1761607680 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))) + 4 +Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 7 31/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[2, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 2 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-3 b/besseltransforms/7-7-3 new file mode 100644 index 0000000..f1a860c --- /dev/null +++ b/besseltransforms/7-7-3 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 3 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x 2 Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -8 c x + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi + 41247931725 E Cos[-- + k x] 288735522075 E Cos[-- + k x] 866206566225 E Cos[-- + k x] 1443677610375 E Cos[-- + k x] 1443677610375 E Cos[-- + k x] 866206566225 E Cos[-- + k x] 288735522075 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 11486475 E Cos[-- + k x] 80405325 E Cos[-- + k x] 241215975 E Cos[-- + k x] 402026625 E Cos[-- + k x] 402026625 E Cos[-- + k x] 241215975 E Cos[-- + k x] 80405325 E Cos[-- + k x] 11486475 E Cos[-- + k x] 45045 E Cos[-- + k x] 315315 E Cos[-- + k x] 945945 E Cos[-- + k x] 1576575 E Cos[-- + k x] 1576575 E Cos[-- + k x] 945945 E Cos[-- + k x] 315315 E Cos[-- + k x] 45045 E Cos[-- + k x] 945 E Cos[-- + k x] 6615 E Cos[-- + k x] 19845 E Cos[-- + k x] 33075 E Cos[-- + k x] 33075 E Cos[-- + k x] 19845 E Cos[-- + k x] 6615 E Cos[-- + k x] 945 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 7 E Sqrt[--] Cos[-- + k x] 21 E Sqrt[--] Cos[-- + k x] 35 E Sqrt[--] Cos[-- + k x] 35 E Sqrt[--] Cos[-- + k x] 21 E Sqrt[--] Cos[-- + k x] 7 E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 8116676342775 E Sin[-- + k x] 24350029028325 E Sin[-- + k x] 40583381713875 E Sin[-- + k x] 40583381713875 E Sin[-- + k x] 24350029028325 E Sin[-- + k x] 8116676342775 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 218243025 E Sin[-- + k x] 1527701175 E Sin[-- + k x] 4583103525 E Sin[-- + k x] 7638505875 E Sin[-- + k x] 7638505875 E Sin[-- + k x] 4583103525 E Sin[-- + k x] 1527701175 E Sin[-- + k x] 218243025 E Sin[-- + k x] 405405 E Sin[-- + k x] 2837835 E Sin[-- + k x] 8513505 E Sin[-- + k x] 14189175 E Sin[-- + k x] 14189175 E Sin[-- + k x] 8513505 E Sin[-- + k x] 2837835 E Sin[-- + k x] 405405 E Sin[-- + k x] 3465 E Sin[-- + k x] 24255 E Sin[-- + k x] 72765 E Sin[-- + k x] 121275 E Sin[-- + k x] 121275 E Sin[-- + k x] 72765 E Sin[-- + k x] 24255 E Sin[-- + k x] 3465 E Sin[-- + k x] 35 E Sin[-- + k x] 245 E Sin[-- + k x] 735 E Sin[-- + k x] 1225 E Sin[-- + k x] 1225 E Sin[-- + k x] 735 E Sin[-- + k x] 245 E Sin[-- + k x] 35 E Sin[-- + k x] + 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 +Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - --------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + ---------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + -------------------------------------------- - -------------------------------------------- + --------------------------------------------- - --------------------------------------------- + --------------------------------------------- - --------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ---------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}. + 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 17/2 7 29/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 13/2 7 25/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 9/2 7 21/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 5/2 7 17/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 7 13/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 19/2 7 31/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 15/2 7 27/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 11/2 7 23/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 7/2 7 19/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 3/2 7 15/2 + 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 3 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-4 b/besseltransforms/7-7-4 new file mode 100644 index 0000000..d3a9a10 --- /dev/null +++ b/besseltransforms/7-7-4 @@ -0,0 +1,9 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 4 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 + E (-1 + E ) (63 (-41829913125 + 5320972800 k x - 2389770240 k x - 11995709440 k x + 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (105411381075 - 22348085760 k x + 44281036800 k x - 58133053440 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])) + 4 +Integrate::idiv: Integral of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 7 31/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[4, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 4 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-5 b/besseltransforms/7-7-5 new file mode 100644 index 0000000..c51b688 --- /dev/null +++ b/besseltransforms/7-7-5 @@ -0,0 +1,10 @@ +Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[5, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 5 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] + + 2 2 4 4 6 6 8 8 + -8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 99 (79857106875 - 15575938560 k x + 28894494720 k x - 38168166400 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]) + -(E (-1 + E ) (8 k x (-376469218125 + 156436600320 k x + 752777625600 k x - 151145938944 k x + 2147483648 k x ) Cos[-- + k x] - ---------------------------------------------------------------------------------------------------------------------)) + 4 Sqrt[2] +Integrate::idiv: Integral of -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}. + 19/2 7 31/2 + 8589934592 k k0 Sqrt[2 Pi] x +Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[5, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 5 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] diff --git a/besseltransforms/7-7-6 b/besseltransforms/7-7-6 new file mode 100644 index 0000000..3ddda62 --- /dev/null +++ b/besseltransforms/7-7-6 @@ -0,0 +1,2 @@ +((k^10*(-693 + 256*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^11)/(2661120*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^11)/(380160*k^6) + (k^10*(-693 + 256*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^11)/(126720*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^11)/(76032*k^6) + (k^10*(-693 + 256*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^11)/(76032*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^11)/(126720*k^6) + (k^10*(-693 + 256*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^11)/(380160*k^6) - (k^10*(-693 + 256*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) + 10*k^8*(-231 + 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3 + 16*k^6*(-231 + 160*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^5 + 32*k^4*(-99 + 80*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^7 + 128*k^2*(-11 + 10*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^9 + 256*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^11)/(2661120*k^6))/k0^7 +SeriesData[k, Infinity, {(6*c^7)/k0^7, (-315*c^8)/(2*k0^7) + ((35*I)*c^7)/k0^6, (2000*c^9)/k0^7 - ((864*I)*c^8)/k0^6 - (96*c^7)/k0^5, (-315*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^7), (77104*c^11)/k0^7 - ((63360*I)*c^10)/k0^6 - (20000*c^9)/k0^5 + ((2880*I)*c^8)/k0^4 + (160*c^7)/k0^3, (-231*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/(16*k0^7), 0, (143*(378720*c^14 - (511840*I)*c^13*k0 - 302211*c^12*k0^2 + (101199*I)*c^11*k0^3 + 20790*c^10*k0^4 - (2625*I)*c^9*k0^5 - 189*c^8*k0^6 + (6*I)*c^7*k0^7))/(32*k0^7)}, 2, 11, 1] diff --git a/besseltransforms/7-7-7 b/besseltransforms/7-7-7 new file mode 100644 index 0000000..96b3cc1 --- /dev/null +++ b/besseltransforms/7-7-7 @@ -0,0 +1,2 @@ +((231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^12)/(10644480*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^12)/(1520640*k^7) + (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^12)/(506880*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^12)/(304128*k^7) + (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^12)/(304128*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^12)/(506880*k^7) + (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^12)/(1520640*k^7) - (231*k^12 + 4*k^10*(693 - 256*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2 + 40*k^8*(231 - 128*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^4 + 64*k^6*(231 - 160*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^6 + 128*k^4*(99 - 80*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^8 + 512*k^2*(11 - 10*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^10 - 1024*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^12)/(10644480*k^7))/k0^7 +SeriesData[k, Infinity, {(7*c^7)/k0^7, (-24*(9*c^8 - (2*I)*c^7*k0))/k0^7, (105*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^7), (-160*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/k0^7, (693*(4819*c^11 - (3960*I)*c^10*k0 - 1250*c^9*k0^2 + (180*I)*c^8*k0^3 + 10*c^7*k0^4))/(16*k0^7), (-64*(14391*c^12 - (14457*I)*c^11*k0 - 5940*c^10*k0^2 + (1250*I)*c^9*k0^3 + 135*c^8*k0^4 - (6*I)*c^7*k0^5))/k0^7, (1001*(73120*c^13 - (86346*I)*c^12*k0 - 43371*c^11*k0^2 + (11880*I)*c^10*k0^3 + 1875*c^9*k0^4 - (162*I)*c^8*k0^5 - 6*c^7*k0^6))/(32*k0^7), 0, (-429*(4992457*c^15 - (7574400*I)*c^14*k0 - 5118400*c^13*k0^2 + (2014740*I)*c^12*k0^3 + 505995*c^11*k0^4 - (83160*I)*c^10*k0^5 - 8750*c^9*k0^6 + (540*I)*c^8*k0^7 + 15*c^7*k0^8))/(128*k0^7)}, 2, 11, 1] diff --git a/misc/finitesqlatzsym-scatter.py b/misc/finitesqlatzsym-scatter.py index 4da7ae7..ccc5898 100755 --- a/misc/finitesqlatzsym-scatter.py +++ b/misc/finitesqlatzsym-scatter.py @@ -231,6 +231,7 @@ if not pargs.nocentre: ypositions -= Ny * dy / 2 xpositions, ypositions = np.meshgrid(xpositions, ypositions, indexing='ij', copy=False) positions=np.stack((xpositions.ravel(),ypositions.ravel()), axis=-1) +positions=positions[np.random.permutation(len(positions))] N = positions.shape[0] kx = np.linspace(pargs.kxmin, pargs.kxmax, num=pargs.kxdensity, endpoint=True) * 2*np.pi / dx @@ -331,7 +332,7 @@ for action in actions: print("%d. momentum %s invalid (k_0=%f), skipping" % (i, str(klist[i]),k_0)) continue kdir = klistdir[i] - phases = np.exp(1j*np.sum(klist2d[i] * positions, axis=-1)) + phases = np.exp(-1j*np.sum(klist2d[i] * positions, axis=-1)) if action == 0 or action is None: pq = np.array(qpms.plane_pq_y(lMax, kdir, xu)).ravel()[TEč] * phases[:, nx] xresult[i] = scat.scatter_partial(0, pq) @@ -346,6 +347,7 @@ for action in actions: if action is None: np.savez(outfile, omega = freq, klist = klist, metadata=metadata, + positions=positions, ab_x=xresult, ab_y=yresult, ab_z=zresult @@ -353,12 +355,14 @@ for action in actions: elif action == 0: np.savez(outfile, omega = freq, klist = klist, metadata=metadata, + positions=positions, ab_x=xresult, ab_y=yresult, ) elif action == 1: np.savez(outfile, omega = freq, klist = klist, metadata=metadata, + positions=positions, ab_z=zresult ) else: diff --git a/qpms/přehled.md b/qpms/přehled.md index 9836baf..b6db483 100644 --- a/qpms/přehled.md +++ b/qpms/přehled.md @@ -10,6 +10,7 @@ scripts_common.py timetrack.py tmatrices.py types.py +svwf.c ## Smíšené / v přepisu scattering.py diff --git a/setup.py b/setup.py index 5ab8365..1208c69 100644 --- a/setup.py +++ b/setup.py @@ -29,6 +29,7 @@ qpms_c = Extension('qpms_c', #'-fopenmp', ], libraries=['gsl', 'blas', 'gslcblas', #'omp' + # TODO resolve the problem with openblas (missing gotoblas symbol) and preferable use other blas library ], runtime_library_dirs=os.environ['LD_LIBRARY_PATH'].split(':') if 'LD_LIBRARY_PATH' in os.environ else [] )