From 0e302d53a17cd32e26528a66c9761e4e58f0d3e4 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Thu, 18 Jan 2018 17:37:36 +0200 Subject: [PATCH] fixed hankel transform formulae for specific kappa, q, n combinations. Former-commit-id: 6c0dae200188c83aa4fe0b2c37d1585ac192f56c --- besseltransforms/klarge/5-1-0 | 4 ++++ besseltransforms/klarge/5-1-1 | 4 ++++ besseltransforms/klarge/5-1-2 | 4 ++++ besseltransforms/klarge/5-2-0 | 0 besseltransforms/klarge/5-2-1 | 4 ++++ besseltransforms/klarge/5-2-2 | 4 ++++ besseltransforms/klarge/runit.sh | 11 +++++++++++ besseltransforms/klarge/vzor.m | 8 ++++++++ besseltransforms/ksmall/5-1-0 | 4 ++++ besseltransforms/ksmall/5-1-1 | 4 ++++ besseltransforms/ksmall/5-1-2 | 4 ++++ besseltransforms/ksmall/5-2-0 | 0 besseltransforms/ksmall/5-2-1 | 4 ++++ besseltransforms/ksmall/5-2-2 | 4 ++++ besseltransforms/ksmall/runit.sh | 11 +++++++++++ besseltransforms/ksmall/vzor.m | 8 ++++++++ besseltransforms/vzor.m | 4 ++-- 17 files changed, 80 insertions(+), 2 deletions(-) create mode 100644 besseltransforms/klarge/5-1-0 create mode 100644 besseltransforms/klarge/5-1-1 create mode 100644 besseltransforms/klarge/5-1-2 create mode 100644 besseltransforms/klarge/5-2-0 create mode 100644 besseltransforms/klarge/5-2-1 create mode 100644 besseltransforms/klarge/5-2-2 create mode 100755 besseltransforms/klarge/runit.sh create mode 100644 besseltransforms/klarge/vzor.m create mode 100644 besseltransforms/ksmall/5-1-0 create mode 100644 besseltransforms/ksmall/5-1-1 create mode 100644 besseltransforms/ksmall/5-1-2 create mode 100644 besseltransforms/ksmall/5-2-0 create mode 100644 besseltransforms/ksmall/5-2-1 create mode 100644 besseltransforms/ksmall/5-2-2 create mode 100755 besseltransforms/ksmall/runit.sh create mode 100644 besseltransforms/ksmall/vzor.m diff --git a/besseltransforms/klarge/5-1-0 b/besseltransforms/klarge/5-1-0 new file mode 100644 index 0000000..76201ee --- /dev/null +++ b/besseltransforms/klarge/5-1-0 @@ -0,0 +1,4 @@ +(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(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)) + 5/(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)) + 1/Sqrt[k^2 - k0^2])/k0 +(-5/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + 10/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - 10/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + 5/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + 1/Sqrt(Power(k,2) - Power(k0,2)))/k0 +SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), -k0/(2*k), k0/2, ((-15*(c - I*k0)^3*(c/k - (I*k0)/k))/8 + (15*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/4 - (15*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/4 + (15*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8)/k0, (3*k0^3)/8, ((25*(c - I*k0)^5*(c/k - (I*k0)/k))/16 - (25*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8 + (25*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8 - (25*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16 + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16)/k0, (5*k0^5)/16, ((-175*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (175*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (175*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (175*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, (35*k0^7)/128, ((315*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (315*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (315*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (315*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1] +(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(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)) + 5/(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)) + 1/Sqrt[k^2 - k0^2])/k0 diff --git a/besseltransforms/klarge/5-1-1 b/besseltransforms/klarge/5-1-1 new file mode 100644 index 0000000..fcae90b --- /dev/null +++ b/besseltransforms/klarge/5-1-1 @@ -0,0 +1,4 @@ +(-k^(-1) - 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(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])) + 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (1 + (I*k0)/Sqrt[k^2 - k0^2])/k)/k0 +(-(1/k) - 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) + 1/(k*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (1 + (Complex(0,1)*k0)/Sqrt(Power(k,2) - Power(k0,2)))/k)/k0 +SeriesData[k, Infinity, {-I/k, I, (-I/2*k0^2)/k, I/2*k0^2, (3*(120*c^5 - I*k0^5))/(8*k*k0), (3*I)/8*k0^4, (-5*(16800*c^7 - (12600*I)*c^6*k0 - 2520*c^5*k0^2 + I*k0^7))/(16*k*k0), (5*I)/16*k0^6, (35*(834120*c^9 - (1134000*I)*c^8*k0 - 604800*c^7*k0^2 + (151200*I)*c^6*k0^3 + 15120*c^5*k0^4 - I*k0^9))/(128*k*k0), (35*I)/128*k0^8}, 1, 11, 1] +(-5*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]) + 10*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]) - 10*(1 - 1/Sqrt[1 + k^2/(3*c - I*k0)^2]) + 5*(1 - 1/Sqrt[1 + k^2/(4*c - I*k0)^2]) + 1/Sqrt[1 + k^2/(5*c - I*k0)^2] + (I*k0)/Sqrt[k^2 - k0^2])/(k*k0) diff --git a/besseltransforms/klarge/5-1-2 b/besseltransforms/klarge/5-1-2 new file mode 100644 index 0000000..e772728 --- /dev/null +++ b/besseltransforms/klarge/5-1-2 @@ -0,0 +1,4 @@ +(-5*(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])) + 10*(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])) + 5*(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])) - 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]) + ((2*I)*k*k0 + (k*(k^2 - 2*k0^2))/Sqrt[k^2 - k0^2])/k^3)/k0 +(-5*(1/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) - (2*(c - Complex(0,1)*k0))/Power(k,2) + (2*(c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (2*(2*c - Complex(0,1)*k0))/Power(k,2) + (2*(2*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) - (2*(3*c - Complex(0,1)*k0))/Power(k,2) + (2*(3*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (2*(4*c - Complex(0,1)*k0))/Power(k,2) + (2*(4*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (2*(5*c - Complex(0,1)*k0))/Power(k,2) - (2*(5*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Complex(0,2)*k*k0 + (k*(Power(k,2) - 2*Power(k0,2)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,3))/k0 +SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), (3*k0)/(2*k), (-3*k0)/2, ((5*c - I*k0)^4/k - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*(-((c - I*k0)^4/k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*(-((2*c - I*k0)^4/k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*(-((3*c - I*k0)^4/k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*(-((4*c - I*k0)^4/k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, (-5*k0^3)/8, ((-3*(5*c - I*k0)^6)/(4*k) + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16 - 5*((3*(c - I*k0)^6)/(4*k) - (5*(c - I*k0)^5*(c/k - (I*k0)/k))/16) + 10*((3*(2*c - I*k0)^6)/(4*k) - (5*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/16) - 10*((3*(3*c - I*k0)^6)/(4*k) - (5*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/16) + 5*((3*(4*c - I*k0)^6)/(4*k) - (5*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16))/k0, (-7*k0^5)/16, ((5*(5*c - I*k0)^8)/(8*k) - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-5*(c - I*k0)^8)/(8*k) + (35*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-5*(2*c - I*k0)^8)/(8*k) + (35*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-5*(3*c - I*k0)^8)/(8*k) + (35*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-5*(4*c - I*k0)^8)/(8*k) + (35*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, (-45*k0^7)/128, ((-35*(5*c - I*k0)^10)/(64*k) + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256 - 5*((35*(c - I*k0)^10)/(64*k) - (63*(c - I*k0)^9*(c/k - (I*k0)/k))/256) + 10*((35*(2*c - I*k0)^10)/(64*k) - (63*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/256) - 10*((35*(3*c - I*k0)^10)/(64*k) - (63*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/256) + 5*((35*(4*c - I*k0)^10)/(64*k) - (63*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256))/k0}, 0, 11, 1] +(-5*(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])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (8*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-8*c + (2*I)*k0)/k^2) - 10*(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) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (4*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-4*c + (2*I)*k0)/k^2) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (10*c - (2*I)*k0)/k^2 + (-10*c + (2*I)*k0)/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + ((2*I)*k*k0 + (k*(k^2 - 2*k0^2))/Sqrt[k^2 - k0^2])/k^3)/k0 diff --git a/besseltransforms/klarge/5-2-0 b/besseltransforms/klarge/5-2-0 new file mode 100644 index 0000000..e69de29 diff --git a/besseltransforms/klarge/5-2-1 b/besseltransforms/klarge/5-2-1 new file mode 100644 index 0000000..2f6c076 --- /dev/null +++ b/besseltransforms/klarge/5-2-1 @@ -0,0 +1,4 @@ +(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-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) + 5*(-1 + 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) + I*k0 + Sqrt[k^2 - k0^2])/(k*k0^2) +(-5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) - (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + Complex(0,1)*k0 + Sqrt(Power(k,2) - Power(k0,2)))/(k*Power(k0,2)) +SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] +(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-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) + 5*(-1 + 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) + I*k0 + Sqrt[k^2 - k0^2])/(k*k0^2) diff --git a/besseltransforms/klarge/5-2-2 b/besseltransforms/klarge/5-2-2 new file mode 100644 index 0000000..b9240a6 --- /dev/null +++ b/besseltransforms/klarge/5-2-2 @@ -0,0 +1,4 @@ +(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-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 - 5*(-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 - k0^2 + I*k0*Sqrt[k^2 - k0^2])/(k^2*k0^2) +(5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - Power(k0,2) + Complex(0,1)*k0*Sqrt(Power(k,2) - Power(k0,2)))/(Power(k,2)*Power(k0,2)) +SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] +(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-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 - 5*(-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 - k0^2 + I*k0*Sqrt[k^2 - k0^2])/(k^2*k0^2) diff --git a/besseltransforms/klarge/runit.sh b/besseltransforms/klarge/runit.sh new file mode 100755 index 0000000..d277388 --- /dev/null +++ b/besseltransforms/klarge/runit.sh @@ -0,0 +1,11 @@ +#!/bin/bash +K=$1 +Q=$2 +N=$3 +module load mathematica +cat - vzor.m <<<" +kk=$K; +qq=$Q; +nn=$N; +" | math -noprompt > "${K}-${Q}-${N}" + diff --git a/besseltransforms/klarge/vzor.m b/besseltransforms/klarge/vzor.m new file mode 100644 index 0000000..6803aa7 --- /dev/null +++ b/besseltransforms/klarge/vzor.m @@ -0,0 +1,8 @@ +$Assumptions = k >= 0 && k > k0 && k0 >= 0 && c >= 0 && n >= 0 ; +f = Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ + I k0 x] x BesselJ[n, k x], {x, + 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}] +CForm[f] +Series[f, {k, \[Infinity], 10}] +Simplify[f] +Quit[ ] diff --git a/besseltransforms/ksmall/5-1-0 b/besseltransforms/ksmall/5-1-0 new file mode 100644 index 0000000..9b2b70d --- /dev/null +++ b/besseltransforms/ksmall/5-1-0 @@ -0,0 +1,4 @@ +(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(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)) + 5/(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)) + I/Sqrt[-k^2 + k0^2])/k0 +(-5/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + 10/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - 10/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + 5/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + Complex(0,1)/Sqrt(-Power(k,2) + Power(k0,2)))/k0 +SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), -k0/(2*k), k0/2, ((-15*(c - I*k0)^3*(c/k - (I*k0)/k))/8 + (15*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/4 - (15*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/4 + (15*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8)/k0, (3*k0^3)/8, ((25*(c - I*k0)^5*(c/k - (I*k0)/k))/16 - (25*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8 + (25*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8 - (25*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16 + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16)/k0, (5*k0^5)/16, ((-175*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (175*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (175*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (175*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, (35*k0^7)/128, ((315*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (315*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (315*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (315*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1] +(-5/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 10/(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)) + 5/(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)) + I/Sqrt[-k^2 + k0^2])/k0 diff --git a/besseltransforms/ksmall/5-1-1 b/besseltransforms/ksmall/5-1-1 new file mode 100644 index 0000000..7cb5ee3 --- /dev/null +++ b/besseltransforms/ksmall/5-1-1 @@ -0,0 +1,4 @@ +(-k^(-1) - 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(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])) + 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (1 - k0/Sqrt[-k^2 + k0^2])/k)/k0 +(-(1/k) - 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/k - 1/(k*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) + 1/(k*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (1 - k0/Sqrt(-Power(k,2) + Power(k0,2)))/k)/k0 +SeriesData[k, Infinity, {-I/k, I, (-I/2*k0^2)/k, I/2*k0^2, (3*(120*c^5 - I*k0^5))/(8*k*k0), (3*I)/8*k0^4, (-5*(16800*c^7 - (12600*I)*c^6*k0 - 2520*c^5*k0^2 + I*k0^7))/(16*k*k0), (5*I)/16*k0^6, (35*(834120*c^9 - (1134000*I)*c^8*k0 - 604800*c^7*k0^2 + (151200*I)*c^6*k0^3 + 15120*c^5*k0^4 - I*k0^9))/(128*k*k0), (35*I)/128*k0^8}, 1, 11, 1] +(-5*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]) + 10*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]) - 10*(1 - 1/Sqrt[1 + k^2/(3*c - I*k0)^2]) + 5*(1 - 1/Sqrt[1 + k^2/(4*c - I*k0)^2]) + 1/Sqrt[1 + k^2/(5*c - I*k0)^2] - k0/Sqrt[-k^2 + k0^2])/(k*k0) diff --git a/besseltransforms/ksmall/5-1-2 b/besseltransforms/ksmall/5-1-2 new file mode 100644 index 0000000..2257754 --- /dev/null +++ b/besseltransforms/ksmall/5-1-2 @@ -0,0 +1,4 @@ +(-5*(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])) + 10*(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])) + 5*(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])) - 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]) + (I*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0 +(-5*(1/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) - (2*(c - Complex(0,1)*k0))/Power(k,2) + (2*(c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (2*(2*c - Complex(0,1)*k0))/Power(k,2) + (2*(2*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) - (2*(3*c - Complex(0,1)*k0))/Power(k,2) + (2*(3*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (2*(4*c - Complex(0,1)*k0))/Power(k,2) + (2*(4*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (2*(5*c - Complex(0,1)*k0))/Power(k,2) - (2*(5*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Complex(0,1)*(Power(k,2) + 2*k0*(-k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/(Power(k,2)*Sqrt(-Power(k,2) + Power(k0,2))))/k0 +SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), (3*k0)/(2*k), (-3*k0)/2, ((5*c - I*k0)^4/k - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*(-((c - I*k0)^4/k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*(-((2*c - I*k0)^4/k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*(-((3*c - I*k0)^4/k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*(-((4*c - I*k0)^4/k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, (-5*k0^3)/8, ((-3*(5*c - I*k0)^6)/(4*k) + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16 - 5*((3*(c - I*k0)^6)/(4*k) - (5*(c - I*k0)^5*(c/k - (I*k0)/k))/16) + 10*((3*(2*c - I*k0)^6)/(4*k) - (5*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/16) - 10*((3*(3*c - I*k0)^6)/(4*k) - (5*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/16) + 5*((3*(4*c - I*k0)^6)/(4*k) - (5*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16))/k0, (-7*k0^5)/16, ((5*(5*c - I*k0)^8)/(8*k) - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-5*(c - I*k0)^8)/(8*k) + (35*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-5*(2*c - I*k0)^8)/(8*k) + (35*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-5*(3*c - I*k0)^8)/(8*k) + (35*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-5*(4*c - I*k0)^8)/(8*k) + (35*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, (-45*k0^7)/128, ((-35*(5*c - I*k0)^10)/(64*k) + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256 - 5*((35*(c - I*k0)^10)/(64*k) - (63*(c - I*k0)^9*(c/k - (I*k0)/k))/256) + 10*((35*(2*c - I*k0)^10)/(64*k) - (63*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/256) - 10*((35*(3*c - I*k0)^10)/(64*k) - (63*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/256) + 5*((35*(4*c - I*k0)^10)/(64*k) - (63*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256))/k0}, 0, 11, 1] +(-5*(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])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (8*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-8*c + (2*I)*k0)/k^2) - 10*(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) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (4*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-4*c + (2*I)*k0)/k^2) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (10*c - (2*I)*k0)/k^2 + (-10*c + (2*I)*k0)/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (I*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0 diff --git a/besseltransforms/ksmall/5-2-0 b/besseltransforms/ksmall/5-2-0 new file mode 100644 index 0000000..e69de29 diff --git a/besseltransforms/ksmall/5-2-1 b/besseltransforms/ksmall/5-2-1 new file mode 100644 index 0000000..a248614 --- /dev/null +++ b/besseltransforms/ksmall/5-2-1 @@ -0,0 +1,4 @@ +(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-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) + 5*(-1 + 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) + I*(k0 - Sqrt[-k^2 + k0^2]))/(k*k0^2) +(-5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*(c - Complex(0,1)*k0) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*(2*c - Complex(0,1)*k0) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*(3*c - Complex(0,1)*k0) + 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*(4*c - Complex(0,1)*k0) - (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*(5*c - Complex(0,1)*k0) + Complex(0,1)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))))/(k*Power(k0,2)) +SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1] +(-5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 10*(-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) + 5*(-1 + 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) + I*(k0 - Sqrt[-k^2 + k0^2]))/(k*k0^2) diff --git a/besseltransforms/ksmall/5-2-2 b/besseltransforms/ksmall/5-2-2 new file mode 100644 index 0000000..a9a4158 --- /dev/null +++ b/besseltransforms/ksmall/5-2-2 @@ -0,0 +1,4 @@ +(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-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 - 5*(-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 - k0*(k0 - Sqrt[-k^2 + k0^2]))/(k^2*k0^2) +(5*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 10*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 10*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 5*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + (-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - k0*(k0 - Sqrt(-Power(k,2) + Power(k0,2))))/(Power(k,2)*Power(k0,2)) +SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1] +(5*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 10*(-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 - 5*(-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 - k0*(k0 - Sqrt[-k^2 + k0^2]))/(k^2*k0^2) diff --git a/besseltransforms/ksmall/runit.sh b/besseltransforms/ksmall/runit.sh new file mode 100755 index 0000000..d277388 --- /dev/null +++ b/besseltransforms/ksmall/runit.sh @@ -0,0 +1,11 @@ +#!/bin/bash +K=$1 +Q=$2 +N=$3 +module load mathematica +cat - vzor.m <<<" +kk=$K; +qq=$Q; +nn=$N; +" | math -noprompt > "${K}-${Q}-${N}" + diff --git a/besseltransforms/ksmall/vzor.m b/besseltransforms/ksmall/vzor.m new file mode 100644 index 0000000..0146350 --- /dev/null +++ b/besseltransforms/ksmall/vzor.m @@ -0,0 +1,8 @@ +$Assumptions = k >= 0 && k < k0 && k0 >= 0 && c >= 0 && n >= 0 ; +f = Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ + I k0 x] x BesselJ[n, k x], {x, + 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}] +CForm[f] +Series[f, {k, \[Infinity], 10}] +Simplify[f] +Quit[ ] diff --git a/besseltransforms/vzor.m b/besseltransforms/vzor.m index 6d76b02..0c1706e 100644 --- a/besseltransforms/vzor.m +++ b/besseltransforms/vzor.m @@ -1,6 +1,6 @@ $Assumptions = k >= 0 && k0 >= 0 && c >= 0 && n >= 0 ; -Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ +Simplify[Refine[Integrate[(1 - Exp[-c x])^\[Kappa] (k0 x)^(-q) Exp[ I k0 x] x BesselJ[n, k x], {x, - 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}] + 0, \[Infinity]}], {\[Kappa] == kk, q == qq, n == nn}]] Series[%, {k, \[Infinity], 10}] Quit[ ]