From b6edd0475529e266d39acd32f962ea6018709906 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Marek=20Ne=C4=8Dada?= Date: Wed, 28 Mar 2018 11:52:50 +0300 Subject: [PATCH] Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 --- besseltransforms/2-1-0 | 4 ++-- besseltransforms/2-1-1 | 4 ++-- besseltransforms/2-1-2 | 4 ++-- besseltransforms/2-2-0 | 9 --------- besseltransforms/2-2-1 | 4 ++-- besseltransforms/2-2-2 | 4 ++-- besseltransforms/2-3-0 | 9 --------- besseltransforms/2-3-1 | 6 +++--- besseltransforms/2-3-2 | 4 ++-- besseltransforms/3-1-0 | 2 ++ besseltransforms/3-1-1 | 2 ++ besseltransforms/3-1-2.REMOVED.git-id | 1 + besseltransforms/3-2-0 | 0 besseltransforms/3-2-1 | 4 ++-- besseltransforms/3-2-2 | 2 ++ besseltransforms/3-3-0 | 9 --------- besseltransforms/3-3-1 | 6 +++--- besseltransforms/3-3-2 | 4 ++-- besseltransforms/4-1-0.REMOVED.git-id | 1 + besseltransforms/4-1-1 | 2 -- besseltransforms/4-1-1.REMOVED.git-id | 1 + besseltransforms/4-1-2 | 2 -- besseltransforms/4-1-2.REMOVED.git-id | 1 + besseltransforms/4-2-0 | 10 +--------- besseltransforms/4-2-1 | 2 ++ besseltransforms/4-2-2 | 4 ++-- besseltransforms/4-3-0 | 9 +-------- besseltransforms/4-3-1 | 9 +-------- besseltransforms/4-3-2 | 4 ++-- besseltransforms/5-1-0 | 2 -- besseltransforms/5-1-0.REMOVED.git-id | 1 + besseltransforms/5-1-1 | 2 -- besseltransforms/5-1-1.REMOVED.git-id | 1 + besseltransforms/5-1-2 | 2 -- besseltransforms/5-1-2.REMOVED.git-id | 1 + besseltransforms/5-2-0 | 16 ++++++++-------- besseltransforms/5-2-1 | 4 ++-- besseltransforms/5-2-2 | 4 ++-- besseltransforms/5-3-0 | 9 +-------- besseltransforms/5-3-1 | 9 +-------- besseltransforms/5-3-2 | 4 ++-- besseltransforms/6-1-0 | 2 -- besseltransforms/6-1-0.REMOVED.git-id | 1 + besseltransforms/6-1-1 | 2 -- besseltransforms/6-1-1.REMOVED.git-id | 1 + besseltransforms/6-1-2 | 2 -- besseltransforms/6-1-2.REMOVED.git-id | 1 + besseltransforms/6-2-0 | 9 +-------- besseltransforms/6-2-1 | 4 ++-- besseltransforms/6-2-2 | 4 ++-- besseltransforms/6-3-0 | 9 +-------- besseltransforms/6-3-1 | 9 +-------- besseltransforms/6-3-2 | 4 ++-- besseltransforms/7-1-0 | 2 -- besseltransforms/7-1-0.REMOVED.git-id | 1 + besseltransforms/7-1-1 | 2 -- besseltransforms/7-1-1.REMOVED.git-id | 1 + besseltransforms/7-1-2 | 2 -- besseltransforms/7-1-2.REMOVED.git-id | 1 + besseltransforms/7-2-0 | 9 +-------- besseltransforms/7-2-1 | 4 ++-- besseltransforms/7-2-2 | 4 ++-- besseltransforms/7-3-0 | 9 +-------- besseltransforms/7-3-1 | 9 +-------- besseltransforms/7-3-2 | 4 ++-- besseltransforms/klarge/5-3-0 | 14 ++++++-------- besseltransforms/klarge/5-3-1 | 2 -- besseltransforms/klarge/5-4-0 | 14 ++++++-------- besseltransforms/klarge/5-4-1 | 12 ++++++------ besseltransforms/klarge/5-5-0 | 14 ++++++++------ besseltransforms/klarge/5-5-1 | 12 ++++++------ besseltransforms/klarge/5-5-2 | 12 ++++++------ besseltransforms/klarge/5-5-3 | 13 +++++++------ 73 files changed, 129 insertions(+), 238 deletions(-) create mode 100644 besseltransforms/3-1-0 create mode 100644 besseltransforms/3-1-1 create mode 100644 besseltransforms/3-1-2.REMOVED.git-id create mode 100644 besseltransforms/3-2-0 create mode 100644 besseltransforms/3-2-2 create mode 100644 besseltransforms/4-1-0.REMOVED.git-id delete mode 100644 besseltransforms/4-1-1 create mode 100644 besseltransforms/4-1-1.REMOVED.git-id delete mode 100644 besseltransforms/4-1-2 create mode 100644 besseltransforms/4-1-2.REMOVED.git-id delete mode 100644 besseltransforms/5-1-0 create mode 100644 besseltransforms/5-1-0.REMOVED.git-id delete mode 100644 besseltransforms/5-1-1 create mode 100644 besseltransforms/5-1-1.REMOVED.git-id delete mode 100644 besseltransforms/5-1-2 create mode 100644 besseltransforms/5-1-2.REMOVED.git-id delete mode 100644 besseltransforms/6-1-0 create mode 100644 besseltransforms/6-1-0.REMOVED.git-id delete mode 100644 besseltransforms/6-1-1 create mode 100644 besseltransforms/6-1-1.REMOVED.git-id delete mode 100644 besseltransforms/6-1-2 create mode 100644 besseltransforms/6-1-2.REMOVED.git-id delete mode 100644 besseltransforms/7-1-0 create mode 100644 besseltransforms/7-1-0.REMOVED.git-id delete mode 100644 besseltransforms/7-1-1 create mode 100644 besseltransforms/7-1-1.REMOVED.git-id delete mode 100644 besseltransforms/7-1-2 create mode 100644 besseltransforms/7-1-2.REMOVED.git-id diff --git a/besseltransforms/2-1-0 b/besseltransforms/2-1-0 index 2c6e1ee..e19fb5b 100644 --- a/besseltransforms/2-1-0 +++ b/besseltransforms/2-1-0 @@ -1,2 +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] +(-2/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (Sqrt[Pi]*(I*Piecewise[{{0, k0^2/k^2 <= 1}}, k/(Sqrt[-k^2 + k0^2]*Sqrt[Pi])] + Piecewise[{{k/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0]))/k)/k0 +SeriesData[k, Infinity, {-(c^2/(k^2*k0)), 0, (3*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (-5*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, (35*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k^2*k0), 0, ((((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))*(2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - (3*I)*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 + (-(c - I*k0)^5/(16*(2*c - I*k0)) + ((c - I*k0)^3*(2*c - I*k0))/16 + ((c - I*k0)*(2*c - I*k0)^3)/16 - (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 + c*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - I*k0*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - 4*c*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + (2*I)*k0*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0)))) + (-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2))*(2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - (3*I)*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 + ((5*(c - I*k0)^7)/(128*(2*c - I*k0)) - ((c - I*k0)^5*(2*c - I*k0))/32 - ((c - I*k0)^3*(2*c - I*k0)^3)/64 - ((c - I*k0)*(2*c - I*k0)^5)/32 + (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 + c*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) - I*k0*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) - 4*c*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))) + (2*I)*k0*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) - (3*I)*c*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0 + ((-7*(c - I*k0)^9)/(256*(2*c - I*k0)) + (5*(c - I*k0)^7*(2*c - I*k0))/256 + ((c - I*k0)^5*(2*c - I*k0)^3)/128 + ((c - I*k0)^3*(2*c - I*k0)^5)/128 + (5*(c - I*k0)*(2*c - I*k0)^7)/256 - (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2 + c*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) - I*k0*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) - 4*c*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0))) + (2*I)*k0*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0)))))/k^2 + ((11*c^4 - (24*I)*c^3*k0 - 12*c^2*k0^2)*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2))/4 - c^2*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2))/((c - I*k0)*(2*c - I*k0)*k0)}, 1, 11, 1] diff --git a/besseltransforms/2-1-1 b/besseltransforms/2-1-1 index d4bbdaa..346813f 100644 --- a/besseltransforms/2-1-1 +++ b/besseltransforms/2-1-1 @@ -1,2 +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] +(k^(-1) - (2*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]))/k - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2]) + Sqrt[Pi]*((I*Piecewise[{{k0/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0])/k + Piecewise[{{(k0*(1 - k0/Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k^2/k0^2 < 1}, {k0/(k*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]/k0))/k0 +Piecewise[{{SeriesData[k, Infinity, {(3*c^2*(c - I*k0))/(k^2*k0), 0, (15*(-3*c^5 + (7*I)*c^4*k0 + 6*c^3*k0^2 - (2*I)*c^2*k0^3))/(4*k^2*k0), 0, (35*(9*c^7 - (31*I)*c^6*k0 - 45*c^5*k0^2 + (35*I)*c^4*k0^3 + 15*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k^2*k0), 0, (105*(-85*c^9 + (381*I)*c^8*k0 + 756*c^7*k0^2 - (868*I)*c^6*k0^3 - 630*c^5*k0^4 + (294*I)*c^4*k0^5 + 84*c^3*k0^6 - (12*I)*c^2*k0^7))/(64*k^2*k0), 0, (693*(93*c^11 - (511*I)*c^10*k0 - 1275*c^9*k0^2 + (1905*I)*c^8*k0^3 + 1890*c^7*k0^4 - (1302*I)*c^6*k0^5 - 630*c^5*k0^6 + (210*I)*c^4*k0^7 + 45*c^3*k0^8 - (5*I)*c^2*k0^9))/(128*k^2*k0)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {I/k^2, 0, (I/2*((-6*I)*c^3 - 6*c^2*k0 + k0^3))/(k^2*k0), 0, ((I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2))))/((c - I*k0)*(2*c - I*k0)) - (k0*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))))/((c - I*k0)*(2*c - I*k0)) + (I*(c - I*k0)*(2*c - I*k0)*((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))))))/k^2)/k0, 0, ((I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))))/((c - I*k0)*(2*c - I*k0)) - ((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)))*((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))))) + (I*(c - I*k0)*(2*c - I*k0)*((-I/16*k0^6)/(c - I*k0) - I/8*k0^4*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + I*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - I/2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I/8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/16*k0^6)/(2*c - I*k0) - I/8*k0^4*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) + I*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))))))/k^2 - (k0*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - (3*I)/8*k0^4*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2)))/((c - I*k0)*(2*c - I*k0)))/k0, 0, (-((((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))*((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0)))))) - ((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)))*((-I/16*k0^6)/(c - I*k0) - I/8*k0^4*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + I*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - I/2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I/8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/16*k0^6)/(2*c - I*k0) - I/8*k0^4*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) + I*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))))) + (I*(c - I*k0)*(2*c - I*k0)*(((-5*I)/128*k0^8)/(c - I*k0) - I/16*k0^6*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) - I/2*k0^2*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + I*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) + k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - I/2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I/8*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 - I/16*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0))) - 2*(((-5*I)/128*k0^8)/(2*c - I*k0) - I/16*k0^6*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))))))/k^2 + (I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - (3*I)/8*k0^4*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2)))/((c - I*k0)*(2*c - I*k0)) - (k0*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*k0^8)/k^2 - (5*I)/16*k0^6*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - (3*I)/8*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I/2*k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2) - I*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2)))/((c - I*k0)*(2*c - I*k0)))/k0, 0, (-((((-3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I/2*k0^2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))*((-I/16*k0^6)/(c - I*k0) - I/8*k0^4*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + I*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - I/2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I/8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/16*k0^6)/(2*c - I*k0) - I/8*k0^4*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) + I*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0)))))) - ((-I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2 - I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)))*(((-5*I)/128*k0^8)/(c - I*k0) - I/16*k0^6*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) - I/2*k0^2*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) + I*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) + k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - I/2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I/8*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 - I/16*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0))) - 2*(((-5*I)/128*k0^8)/(2*c - I*k0) - I/16*k0^6*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))))) + (I*(c - I*k0)*(2*c - I*k0)*(((-7*I)/256*k0^10)/(c - I*k0) - (5*I)/128*k0^8*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) - I/16*k0^6*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) - I/8*k0^4*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - I/2*k0^2*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) + I*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) + k0*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) - I/2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - I/8*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4 - I/16*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6 - (5*I)/128*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8 - ((7*I)/256*k0^10)/((c - I*k0)*(2*c - I*k0))) - 2*(((-7*I)/256*k0^10)/(2*c - I*k0) - (5*I)/128*k0^8*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) - I/16*k0^6*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0))) - I/8*k0^4*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) - I/2*k0^2*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))) + I*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0))))))/k^2 - ((-I/8*k0^4)/(c - I*k0) - I/2*k0^2*((c - I*k0)/2 - k0^2/(2*(c - I*k0))) + I*(-(c - I*k0)^3/8 - ((c - I*k0)*k0^2)/4 - k0^4/(8*(c - I*k0))) + k0*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*k0*(I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0))) - I/2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0))) - 2*((-I/8*k0^4)/(2*c - I*k0) - I/2*k0^2*((2*c - I*k0)/2 - k0^2/(2*(2*c - I*k0))) + I*(-(2*c - I*k0)^3/8 - ((2*c - I*k0)*k0^2)/4 - k0^4/(8*(2*c - I*k0)))))*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - (3*I)/8*k0^4*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2)) + (I/2*(6*c^3 - I*c^2*k0 + 6*c*k0^2 - (3*I)*k0^3)*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*k0^8)/k^2 - (5*I)/16*k0^6*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - (3*I)/8*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I/2*k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2) - I*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2)))/((c - I*k0)*(2*c - I*k0)) - (k0*(((-63*I)/256*(c - I*k0)*(2*c - I*k0)*k0^10)/k^2 - (35*I)/128*k0^8*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2)) - (5*I)/16*k0^6*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - (3*I)/8*k0^4*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*k0^6)/(16*k^2) - (5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k) + (k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/2) - I/2*k0^2*((5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*k0^8)/(128*k^2) + (35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64 + (3*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 + (k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/2) - I*((35*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^8)/128 + (63*(c - I*k0)*(2*c - I*k0)*k0^10)/(256*k^2) - (63*(c - I*k0)^10*(2*c - I*k0)*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^8*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^3*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(256*k) - (63*(c - I*k0)*(2*c - I*k0)^10*((2*c)/k - (I*k0)/k))/(256*k) - (15*(c - I*k0)^6*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128 - (15*(c - I*k0)^4*(2*c - I*k0)^6*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128 + (5*k0^6*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/16 + (3*k0^4*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/8 + (k0^2*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/2)))/((c - I*k0)*(2*c - I*k0)))/k0}, 0, 11, 1]] diff --git a/besseltransforms/2-1-2 b/besseltransforms/2-1-2 index e4532d3..38fc03e 100644 --- a/besseltransforms/2-1-2 +++ b/besseltransforms/2-1-2 @@ -1,2 +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] +(-2/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (4*(c - I*k0))/k^2 - (4*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) + 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 + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (k0*(k^2 - 2*k0^2))/(k^3*Sqrt[Pi - (k0^2*Pi)/k^2])] + I*Piecewise[{{(k0*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*k0^2)/(k^2*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]))/k0)/k0 +Piecewise[{{SeriesData[k, Infinity, {(3*c^2)/(k^2*k0), 0, (-5*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (7*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, (-45*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k^2*k0), 0, (77*(511*c^10 - (2550*I)*c^9*k0 - 5715*c^8*k0^2 + (7560*I)*c^7*k0^3 + 6510*c^6*k0^4 - (3780*I)*c^5*k0^5 - 1470*c^4*k0^6 + (360*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k^2*k0)}, 1, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {(3*c^2)/(k^2*k0), 0, (-5*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (7*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, ((-I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2)) - (I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2)*((2*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) + 3*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 - (4*I)*c^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - 6*c*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^3 + (2*I)*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 + 8*c^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - (16*I)*c^2*k0*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 10*c*k0^2*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) + (2*I)*k0^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 8*c^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + (20*I)*c^2*k0*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + 16*c*k0^2*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) - (4*I)*k0^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + c*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - I*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 4*c*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (2*I)*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0))) - (I*(c - I*k0)*(2*c - I*k0)*((2*I)*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) + 3*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 - (4*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - 6*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^3 + (2*I)*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4 + 8*c^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - (16*I)*c^2*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 10*c*k0^2*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) + (2*I)*k0^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 8*c^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (20*I)*c^2*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + 16*c*k0^2*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) - (4*I)*k0^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + c*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - I*k0*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 4*c*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + (2*I)*k0*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0))))/k^2 - I/4*(5*c^4 - (24*I)*c^3*k0 - 12*c^2*k0^2)*(-I/2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2 - ((3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))) + (3*I)*c^2*((-3*I)/8*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4 - ((5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k))))/((c - I*k0)*(2*c - I*k0)*k0), 0, ((-I*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2)) - (I/2*(c - I*k0)*(2*c - I*k0)*k0^2)/k^2)*((2*I)*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) + 3*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 - (4*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - 6*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^3 + (2*I)*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4 + 8*c^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - (16*I)*c^2*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 10*c*k0^2*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) + (2*I)*k0^3*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 8*c^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (20*I)*c^2*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + 16*c*k0^2*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) - (4*I)*k0^3*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + c*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - I*k0*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 4*c*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + (2*I)*k0*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0))) - (I*(c - I*k0)*(2*c - I*k0)*((2*I)*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) + 3*c*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0 - (4*I)*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 - I*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2 - 6*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^3 + (2*I)*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4 + 8*c^3*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - (16*I)*c^2*k0*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 10*c*k0^2*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) + (2*I)*k0^3*((-5*I)/128*(c - I*k0)^7 - I/32*(c - I*k0)^5*k0^2 + I/64*(c - I*k0)^3*k0^4 - I/32*(c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(c - I*k0)) - 8*c^3*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + (20*I)*c^2*k0*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + 16*c*k0^2*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) - (4*I)*k0^3*((-5*I)/128*(2*c - I*k0)^7 - I/32*(2*c - I*k0)^5*k0^2 + I/64*(2*c - I*k0)^3*k0^4 - I/32*(2*c - I*k0)*k0^6 - ((5*I)/128*k0^8)/(2*c - I*k0)) + c*((7*I)/256*(c - I*k0)^9 + (5*I)/256*(c - I*k0)^7*k0^2 - I/128*(c - I*k0)^5*k0^4 + I/128*(c - I*k0)^3*k0^6 - (5*I)/256*(c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(c - I*k0)) - I*k0*((7*I)/256*(c - I*k0)^9 + (5*I)/256*(c - I*k0)^7*k0^2 - I/128*(c - I*k0)^5*k0^4 + I/128*(c - I*k0)^3*k0^6 - (5*I)/256*(c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(c - I*k0)) - 4*c*((7*I)/256*(2*c - I*k0)^9 + (5*I)/256*(2*c - I*k0)^7*k0^2 - I/128*(2*c - I*k0)^5*k0^4 + I/128*(2*c - I*k0)^3*k0^6 - (5*I)/256*(2*c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(2*c - I*k0)) + (2*I)*k0*((7*I)/256*(2*c - I*k0)^9 + (5*I)/256*(2*c - I*k0)^7*k0^2 - I/128*(2*c - I*k0)^5*k0^4 + I/128*(2*c - I*k0)^3*k0^6 - (5*I)/256*(2*c - I*k0)*k0^8 - ((7*I)/256*k0^10)/(2*c - I*k0))))/k^2 + ((2*I)*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) + 3*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 - (4*I)*c^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2 - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 - 6*c*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^3 + (2*I)*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4 + 8*c^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - (16*I)*c^2*k0*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 10*c*k0^2*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) + (2*I)*k0^3*(-I/8*(c - I*k0)^3 - I/4*(c - I*k0)*k0^2 - (I/8*k0^4)/(c - I*k0)) - 8*c^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + (20*I)*c^2*k0*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + 16*c*k0^2*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) - (4*I)*k0^3*(-I/8*(2*c - I*k0)^3 - I/4*(2*c - I*k0)*k0^2 - (I/8*k0^4)/(2*c - I*k0)) + c*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - I*k0*(I/16*(c - I*k0)^5 + I/16*(c - I*k0)^3*k0^2 - I/16*(c - I*k0)*k0^4 - (I/16*k0^6)/(c - I*k0)) - 4*c*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)) + (2*I)*k0*(I/16*(2*c - I*k0)^5 + I/16*(2*c - I*k0)^3*k0^2 - I/16*(2*c - I*k0)*k0^4 - (I/16*k0^6)/(2*c - I*k0)))*(-I/2*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2 - ((3*I)/8*(c - I*k0)*(2*c - I*k0)*k0^4)/k^2 - I*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))) - I/4*(5*c^4 - (24*I)*c^3*k0 - 12*c^2*k0^2)*((-3*I)/8*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^4 - ((5*I)/16*(c - I*k0)*(2*c - I*k0)*k0^6)/k^2 - I/2*k0^2*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k))) + (3*I)*c^2*((-5*I)/16*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^6 - ((35*I)/128*(c - I*k0)*(2*c - I*k0)*k0^8)/k^2 - (3*I)/8*k0^4*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)) - I/2*k0^2*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)) - I*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64)))/((c - I*k0)*(2*c - I*k0)*k0)}, 1, 11, 1]] diff --git a/besseltransforms/2-2-0 b/besseltransforms/2-2-0 index eb7788f..e69de29 100644 --- a/besseltransforms/2-2-0 +++ b/besseltransforms/2-2-0 @@ -1,9 +0,0 @@ -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 index 290b99a..ef9e915 100644 --- a/besseltransforms/2-2-1 +++ b/besseltransforms/2-2-1 @@ -1,2 +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] +((-2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2 +Piecewise[{{SeriesData[k, Infinity, {c^2/k0^2, 0, (3*c^2)/2 - (7*c^4)/(4*k0^2) + ((3*I)*c^3)/k0, 0, (31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4)/(8*k0^2), 0, (-5*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (7*(511*c^10 - (2550*I)*c^9*k0 - 5715*c^8*k0^2 + (7560*I)*c^7*k0^3 + 6510*c^6*k0^4 - (3780*I)*c^5*k0^5 - 1470*c^4*k0^6 + (360*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, (2*c^2 + k0^2)/(2*k0^2), 0, ((c*(c - I*k0)^3)/4 - (c*(2*c - I*k0)^3)/4 - I/4*(c - I*k0)^3*k0 + I/8*(2*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/8 + (c*(2*c - I*k0)^5)/8 + I/8*(c - I*k0)^5*k0 - I/16*(2*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/64 - (5*c*(2*c - I*k0)^7)/64 - (5*I)/64*(c - I*k0)^7*k0 + (5*I)/128*(2*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/128 + (7*c*(2*c - I*k0)^9)/128 + (7*I)/128*(c - I*k0)^9*k0 - (7*I)/256*(2*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/2-2-2 b/besseltransforms/2-2-2 index 42245d6..16eff75 100644 --- a/besseltransforms/2-2-2 +++ b/besseltransforms/2-2-2 @@ -1,2 +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] +(-1 + (4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2) +SeriesData[k, Infinity, {(2*c^2)/k0^2, (-3*(c^3 - I*c^2*k0))/k0^2, 0, (5*(3*c^5 - (7*I)*c^4*k0 - 6*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), 0, (-7*(9*c^7 - (31*I)*c^6*k0 - 45*c^5*k0^2 + (35*I)*c^4*k0^3 + 15*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (15*(85*c^9 - (381*I)*c^8*k0 - 756*c^7*k0^2 + (868*I)*c^6*k0^3 + 630*c^5*k0^4 - (294*I)*c^4*k0^5 - 84*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1] diff --git a/besseltransforms/2-3-0 b/besseltransforms/2-3-0 index 14287a6..e69de29 100644 --- a/besseltransforms/2-3-0 +++ b/besseltransforms/2-3-0 @@ -1,9 +0,0 @@ -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 index 125bafb..42b69b8 100644 --- a/besseltransforms/2-3-1 +++ b/besseltransforms/2-3-1 @@ -1,9 +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] +Integrate[(E^(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] - -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 + -2 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}] +Series[Integrate[(E^(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], {k, Infinity, 10}] diff --git a/besseltransforms/2-3-2 b/besseltransforms/2-3-2 index 78fb0ed..52a4158 100644 --- a/besseltransforms/2-3-2 +++ b/besseltransforms/2-3-2 @@ -1,2 +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] +(-4*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (8*(-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*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3) +SeriesData[k, Infinity, {c^2/k0^3, (-2*(c^3 - I*c^2*k0))/k0^3, (7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2)/(4*k0^3), 0, (-31*c^6 + (90*I)*c^5*k0 + 105*c^4*k0^2 - (60*I)*c^3*k0^3 - 15*c^2*k0^4)/(24*k0^3), 0, (127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6)/(64*k0^3), 0, (-511*c^10 + (2550*I)*c^9*k0 + 5715*c^8*k0^2 - (7560*I)*c^7*k0^3 - 6510*c^6*k0^4 + (3780*I)*c^5*k0^5 + 1470*c^4*k0^6 - (360*I)*c^3*k0^7 - 45*c^2*k0^8)/(128*k0^3)}, 1, 11, 1] diff --git a/besseltransforms/3-1-0 b/besseltransforms/3-1-0 new file mode 100644 index 0000000..2dd4e66 --- /dev/null +++ b/besseltransforms/3-1-0 @@ -0,0 +1,2 @@ +(-3/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 3/(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)) + (Sqrt[Pi]*(I*Piecewise[{{0, k0^2/k^2 <= 1}}, k/(Sqrt[-k^2 + k0^2]*Sqrt[Pi])] + Piecewise[{{k/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0]))/k)/k0 +SeriesData[k, Infinity, {(-9*(3*c^4 - (2*I)*c^3*k0))/(2*k^3*k0), 0, ((-9*(3*c^4 - (2*I)*c^3*k0)*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))/2 + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))))/k^3)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*(6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))))/k^3 - (9*(3*c^4 - (2*I)*c^3*k0)*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*(6*c^3*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + k0^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + (6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - (9*(3*c^4 - (2*I)*c^3*k0)*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2))/2)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*(6*c^3*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + k0^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(6*c^3*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)))/(3*c - I*k0) + (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*(3*c - I*k0))/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^9)/256 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(2*c - I*k0))) + k0^2*((-21*(c - I*k0)^11)/(1024*(2*c - I*k0)) + (7*(c - I*k0)^9*(2*c - I*k0))/512 + (5*(c - I*k0)^7*(2*c - I*k0)^3)/1024 + ((c - I*k0)^5*(2*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(2*c - I*k0)^7)/1024 + (7*(c - I*k0)*(2*c - I*k0)^9)/512 - (21*(2*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-21*(c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(c - I*k0)^9*(3*c - I*k0))/512 + (5*(c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-21*(c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(c - I*k0)^9*(3*c - I*k0))/512 + (5*(c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-21*(c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(c - I*k0)^9*(3*c - I*k0))/512 + (5*(c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(c - I*k0)) - (((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)))*k0^2)/2 - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^4)/8 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^6)/16 - (5*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^8)/128 - (7*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-21*(2*c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(2*c - I*k0)^9*(3*c - I*k0))/512 + (5*(2*c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((2*c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(2*c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(2*c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(2*c - I*k0)) - (((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)))*k0^2)/2 - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^6)/16 - (5*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^8)/128 - (7*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-21*(2*c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(2*c - I*k0)^9*(3*c - I*k0))/512 + (5*(2*c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((2*c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(2*c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(2*c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(2*c - I*k0)) - (((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)))*k0^2)/2 - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^6)/16 - (5*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^8)/128 - (7*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-21*(2*c - I*k0)^11)/(1024*(3*c - I*k0)) + (7*(2*c - I*k0)^9*(3*c - I*k0))/512 + (5*(2*c - I*k0)^7*(3*c - I*k0)^3)/1024 + ((2*c - I*k0)^5*(3*c - I*k0)^5)/256 + (5*(2*c - I*k0)^3*(3*c - I*k0)^7)/1024 + (7*(2*c - I*k0)*(3*c - I*k0)^9)/512 - (21*(3*c - I*k0)^11)/(1024*(2*c - I*k0)) - (((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)))*k0^2)/2 - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^6)/16 - (5*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^8)/128 - (7*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^10)/256 - (21*k0^12)/(1024*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + (6*c^3*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))))*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) + (6*c^3*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - (11*I)*c^2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - 6*c*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^3 - 2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + (3*I)*c*k0*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + 9*c^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - (12*I)*c*k0*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 3*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - 18*c^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + (15*I)*c*k0*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + 3*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - (9*(3*c^4 - (2*I)*c^3*k0)*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2))/2)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0)}, 2, 11, 1] diff --git a/besseltransforms/3-1-1 b/besseltransforms/3-1-1 new file mode 100644 index 0000000..2c31de2 --- /dev/null +++ b/besseltransforms/3-1-1 @@ -0,0 +1,2 @@ +(-k^(-1) - (3*(1 - 1/Sqrt[1 + k^2/(c - I*k0)^2]))/k + (3*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]))/k + 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2]) + Sqrt[Pi]*((I*Piecewise[{{k0/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0])/k + Piecewise[{{(k0*(1 - k0/Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k^2/k0^2 < 1}, {k0/(k*Sqrt[Pi]), k^2/k0^2 > 1}}, 0]/k0))/k0 +Piecewise[{{SeriesData[k, Infinity, {(-3*c^3)/(k^3*k0), 0, (-45*(-5*c^5 + (6*I)*c^4*k0 + 2*c^3*k0^2))/(4*k^3*k0), 0, (-105*(43*c^7 - (90*I)*c^6*k0 - 75*c^5*k0^2 + (30*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k^3*k0), 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)) - 3*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + 3*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)) - 3*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) + 3*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + (3*(47*c^5 - (66*I)*c^4*k0 - 22*c^3*k0^2)*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/(4*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)) - (3*c^3*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) + I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)) - 3*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) + 3*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) + I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)))*k0 - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0)) - 3*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0))) + 3*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0)))))/k^3 + ((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) + I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)) - 3*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + 3*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) + (3*(47*c^5 - (66*I)*c^4*k0 - 22*c^3*k0^2)*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2))/(4*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)) - (3*c^3*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0}, 1, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {I/k^3, 0, (I/2*((6*I)*c^3 + k0^3))/(k^3*k0), 0, (-((((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3))))/((2*c - I*k0)*(3*c - I*k0))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - (k0*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, (-(((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))*((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0)))))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*((I/16*k0^6)/((c - I*k0)*(2*c - I*k0)) + I/8*k0^4*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)) - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - I/2*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/16*k0^6)/((c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) + I*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/16*k0^6)/((2*c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) + I*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - (((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)))/((2*c - I*k0)*(3*c - I*k0)) - (k0*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/k^3 - (3*I)/8*k0^4*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I/2*k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, (-(((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))*((I/16*k0^6)/((c - I*k0)*(2*c - I*k0)) + I/8*k0^4*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)) - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - I/2*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/16*k0^6)/((c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) + I*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/16*k0^6)/((2*c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) + I*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)) + I/16*k0^6*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/8*k0^4*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4 - I/16*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*(((-5*I)/128*k0^8)/((c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + I*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0)))) - 3*(((-5*I)/128*k0^8)/((2*c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - ((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0)))))*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)) - (((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/k^3 - (3*I)/8*k0^4*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I/2*k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)))/((2*c - I*k0)*(3*c - I*k0)) - (k0*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/k^3 - (5*I)/16*k0^6*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - (3*I)/8*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I/2*k0^2*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - I*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0, 0, (-(((-I/2*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/k^3 - I*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)))*(((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)) + I/16*k0^6*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/8*k0^4*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) - I*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) + k0*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^4 - I/16*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^6 - ((5*I)/128*k0^8)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*(((-5*I)/128*k0^8)/((c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) + I*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0)))) - 3*(((-5*I)/128*k0^8)/((2*c - I*k0)*(3*c - I*k0)) - I/16*k0^6*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/8*k0^4*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) + I*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0)))))) + (I*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*(((7*I)/256*k0^10)/((c - I*k0)*(2*c - I*k0)) + (5*I)/128*k0^8*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/16*k0^6*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + I/8*k0^4*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(2*c - I*k0))) - I*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0))) + k0*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0)) - ((((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^6)/16 - (5*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))/(3*c - I*k0) + (((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0)^3)/8 + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^7)/128 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)*(2*c - I*k0))) - I/2*(((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*(3*c - I*k0))/2 - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0)^3)/8 + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^5)/16 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)))*k0^4 - I/16*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^6 - (5*I)/128*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^8 - ((7*I)/256*k0^10)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*(((-7*I)/256*k0^10)/((c - I*k0)*(3*c - I*k0)) - (5*I)/128*k0^8*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/16*k0^6*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) - I/8*k0^4*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)) - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^2)/2 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^4)/8 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(c - I*k0)*(3*c - I*k0))) + I*((7*(c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(c - I*k0)^7*(3*c - I*k0))/256 - ((c - I*k0)^5*(3*c - I*k0)^3)/128 - ((c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(c - I*k0)) - (((-5*(c - I*k0)^7)/(128*(3*c - I*k0)) + ((c - I*k0)^5*(3*c - I*k0))/32 + ((c - I*k0)^3*(3*c - I*k0)^3)/64 + ((c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(c - I*k0)))*k0^2)/2 - (((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)))*k0^4)/8 - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^6)/16 - (5*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(c - I*k0)*(3*c - I*k0)))) - 3*(((-7*I)/256*k0^10)/((2*c - I*k0)*(3*c - I*k0)) - (5*I)/128*k0^8*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/16*k0^6*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) - I/8*k0^4*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)) - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^2)/2 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^4)/8 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^6)/16 - (5*k0^8)/(128*(2*c - I*k0)*(3*c - I*k0))) + I*((7*(2*c - I*k0)^9)/(256*(3*c - I*k0)) - (5*(2*c - I*k0)^7*(3*c - I*k0))/256 - ((2*c - I*k0)^5*(3*c - I*k0)^3)/128 - ((2*c - I*k0)^3*(3*c - I*k0)^5)/128 - (5*(2*c - I*k0)*(3*c - I*k0)^7)/256 + (7*(3*c - I*k0)^9)/(256*(2*c - I*k0)) - (((-5*(2*c - I*k0)^7)/(128*(3*c - I*k0)) + ((2*c - I*k0)^5*(3*c - I*k0))/32 + ((2*c - I*k0)^3*(3*c - I*k0)^3)/64 + ((2*c - I*k0)*(3*c - I*k0)^5)/32 - (5*(3*c - I*k0)^7)/(128*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)))*k0^4)/8 - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^6)/16 - (5*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^8)/128 - (7*k0^10)/(256*(2*c - I*k0)*(3*c - I*k0))))))/k^3 - ((I/16*k0^6)/((c - I*k0)*(2*c - I*k0)) + I/8*k0^4*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) + I/2*k0^2*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) - I*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0))) + k0*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0)) - (((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*(((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))/(3*c - I*k0) + ((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))*(3*c - I*k0))/2 - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0)^3)/8 + (3*c - I*k0)^5/(16*(c - I*k0)*(2*c - I*k0))) - I/2*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)))*k0^2 - I/8*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^4 - (I/16*k0^6)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/16*k0^6)/((c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0))) + I*((c - I*k0)^5/(16*(3*c - I*k0)) - ((c - I*k0)^3*(3*c - I*k0))/16 - ((c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(c - I*k0)) - ((-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)))*k0^2)/2 - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^4)/8 - k0^6/(16*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/16*k0^6)/((2*c - I*k0)*(3*c - I*k0)) - I/8*k0^4*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) - I/2*k0^2*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0))) + I*((2*c - I*k0)^5/(16*(3*c - I*k0)) - ((2*c - I*k0)^3*(3*c - I*k0))/16 - ((2*c - I*k0)*(3*c - I*k0)^3)/16 + (3*c - I*k0)^5/(16*(2*c - I*k0)) - ((-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)))*k0^2)/2 - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^4)/8 - k0^6/(16*(2*c - I*k0)*(3*c - I*k0)))))*(((-3*I)/8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/k^3 - I/2*k0^2*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k)) - ((I/8*k0^4)/((c - I*k0)*(2*c - I*k0)) + I/2*k0^2*((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(2*c - I*k0))) - I*(-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0))) + k0*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0)) - ((((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) - I*k0*(I*((-(c - I*k0)^3/(8*(2*c - I*k0)) + ((c - I*k0)*(2*c - I*k0))/4 - (2*c - I*k0)^3/(8*(c - I*k0)))/(3*c - I*k0) + (((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))*(3*c - I*k0))/2 - (3*c - I*k0)^3/(8*(c - I*k0)*(2*c - I*k0))) - I/2*(((c - I*k0)/(2*(2*c - I*k0)) + (2*c - I*k0)/(2*(c - I*k0)))/(3*c - I*k0) + (3*c - I*k0)/(2*(c - I*k0)*(2*c - I*k0)))*k0^2 - (I/8*k0^4)/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0))) + 3*((-I/8*k0^4)/((c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)) - k0^2/(2*(c - I*k0)*(3*c - I*k0))) + I*(-(c - I*k0)^3/(8*(3*c - I*k0)) + ((c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(c - I*k0)) - (((c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(c - I*k0)))*k0^2)/2 - k0^4/(8*(c - I*k0)*(3*c - I*k0)))) - 3*((-I/8*k0^4)/((2*c - I*k0)*(3*c - I*k0)) - I/2*k0^2*((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)) - k0^2/(2*(2*c - I*k0)*(3*c - I*k0))) + I*(-(2*c - I*k0)^3/(8*(3*c - I*k0)) + ((2*c - I*k0)*(3*c - I*k0))/4 - (3*c - I*k0)^3/(8*(2*c - I*k0)) - (((2*c - I*k0)/(2*(3*c - I*k0)) + (3*c - I*k0)/(2*(2*c - I*k0)))*k0^2)/2 - k0^4/(8*(2*c - I*k0)*(3*c - I*k0)))))*(((-5*I)/16*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/k^3 - (3*I)/8*k0^4*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - I/2*k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2)) - (((3*I)*c^2 + 4*c*k0 - (2*I)*k0^2)*(((-35*I)/128*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/k^3 - (5*I)/16*k0^6*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - (3*I)/8*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - I/2*k0^2*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - I*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2)))/((2*c - I*k0)*(3*c - I*k0)) - (k0*(((-63*I)/256*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^10)/k^3 - (35*I)/128*k0^8*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3) + ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^2)/(2*k^3)) - (5*I)/16*k0^6*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + ((((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^4)/(8*k^3) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k) - (3*I)/8*k0^4*((3*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^4)/8 + (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^6)/(16*k^3) + (3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k + (k0^2*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/2) - I/2*k0^2*((5*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^6)/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^8)/(128*k^3) - (5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k + (3*k0^4*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/8 + (k0^2*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/2) - I*((35*(((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0))/k - ((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^3)/(2*k^3))*k0^8)/128 + (63*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)*k0^10)/(256*k^3) + (35*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/128 - (63*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^10*((3*c)/k - (I*k0)/k))/(256*k^2) - (5*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/16 + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/8 - ((3*c - I*k0)^3*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/(2*k) + ((3*c - I*k0)*((-63*(c - I*k0)^10*(2*c - I*k0)*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^8*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(256*k) - (35*(c - I*k0)^3*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(256*k) - (63*(c - I*k0)*(2*c - I*k0)^10*((2*c)/k - (I*k0)/k))/(256*k) - (15*(c - I*k0)^6*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128 - (15*(c - I*k0)^4*(2*c - I*k0)^6*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/128))/k + (5*k0^6*(-((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^3)/(2*k) + (3*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/(8*k^2) + ((3*c - I*k0)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/k))/16 + (3*k0^4*((3*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8 - (5*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/(16*k^2) - ((3*c - I*k0)^3*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/(2*k) + ((3*c - I*k0)*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/k))/8 + (k0^2*((-5*(-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16 + (35*(c - I*k0)*(2*c - I*k0)*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/(128*k^2) + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k)*(((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k)))/8 - ((3*c - I*k0)^3*((-5*(c - I*k0)^6*(2*c - I*k0)*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^4*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(16*k) - (3*(c - I*k0)^3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(16*k) - (5*(c - I*k0)*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(16*k)))/(2*k) + ((3*c - I*k0)*((35*(c - I*k0)^8*(2*c - I*k0)*(c/k - (I*k0)/k))/(128*k) + (5*(c - I*k0)^6*(2*c - I*k0)^3*(c/k - (I*k0)/k))/(32*k) + (5*(c - I*k0)^3*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/(32*k) + (35*(c - I*k0)*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/(128*k) + (9*(c - I*k0)^4*(2*c - I*k0)^4*(c/k - (I*k0)/k)*((2*c)/k - (I*k0)/k))/64))/k))/2)))/((c - I*k0)*(2*c - I*k0)*(3*c - I*k0)))/k0}, -1, 11, 1]] diff --git a/besseltransforms/3-1-2.REMOVED.git-id b/besseltransforms/3-1-2.REMOVED.git-id new file mode 100644 index 0000000..0550948 --- /dev/null +++ b/besseltransforms/3-1-2.REMOVED.git-id @@ -0,0 +1 @@ +9a2ec0ef6771d8a7db72ddc960cbd1172c4c24e2 \ No newline at end of file diff --git a/besseltransforms/3-2-0 b/besseltransforms/3-2-0 new file mode 100644 index 0000000..e69de29 diff --git a/besseltransforms/3-2-1 b/besseltransforms/3-2-1 index a49536b..d3994f1 100644 --- a/besseltransforms/3-2-1 +++ b/besseltransforms/3-2-1 @@ -1,2 +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] +(-6*(-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) - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) +Piecewise[{{SeriesData[k, Infinity, {(9*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^2), 0, (-105*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/8 - (3*c*(2*c - I*k0)^3)/4 + (3*c*(3*c - I*k0)^3)/8 - (3*I)/8*(c - I*k0)^3*k0 + (3*I)/8*(2*c - I*k0)^3*k0 - I/8*(3*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/16 + (3*c*(2*c - I*k0)^5)/8 - (3*c*(3*c - I*k0)^5)/16 + (3*I)/16*(c - I*k0)^5*k0 - (3*I)/16*(2*c - I*k0)^5*k0 + I/16*(3*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/128 - (15*c*(2*c - I*k0)^7)/64 + (15*c*(3*c - I*k0)^7)/128 - (15*I)/128*(c - I*k0)^7*k0 + (15*I)/128*(2*c - I*k0)^7*k0 - (5*I)/128*(3*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/256 + (21*c*(2*c - I*k0)^9)/128 - (21*c*(3*c - I*k0)^9)/256 + (21*I)/256*(c - I*k0)^9*k0 - (21*I)/256*(2*c - I*k0)^9*k0 + (7*I)/256*(3*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/3-2-2 b/besseltransforms/3-2-2 new file mode 100644 index 0000000..fbfe2c8 --- /dev/null +++ b/besseltransforms/3-2-2 @@ -0,0 +1,2 @@ +(-1 + (6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2) +SeriesData[k, Infinity, {(3*c^3)/k0^2, 0, (-15*(5*c^5 - (6*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^2), 0, (21*(43*c^7 - (90*I)*c^6*k0 - 75*c^5*k0^2 + (30*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^2), 0, (-15*(3025*c^9 - (8694*I)*c^8*k0 - 10836*c^7*k0^2 + (7560*I)*c^6*k0^3 + 3150*c^5*k0^4 - (756*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^2)}, 3, 11, 1] diff --git a/besseltransforms/3-3-0 b/besseltransforms/3-3-0 index f679ead..e69de29 100644 --- a/besseltransforms/3-3-0 +++ b/besseltransforms/3-3-0 @@ -1,9 +0,0 @@ -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 index a06b92b..1c42766 100644 --- a/besseltransforms/3-3-1 +++ b/besseltransforms/3-3-1 @@ -1,9 +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] +Integrate[(E^(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] - -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 + -3 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}] +Series[Integrate[(E^(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], {k, Infinity, 10}] diff --git a/besseltransforms/3-3-2 b/besseltransforms/3-3-2 index 7a2c082..799bd6d 100644 --- a/besseltransforms/3-3-2 +++ b/besseltransforms/3-3-2 @@ -1,2 +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] +(6*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 6*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 2*(3 - 2*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)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3) +SeriesData[k, Infinity, {(2*c^3)/k0^3, (-9*c^4)/(2*k0^3) + ((3*I)*c^3)/k0^2, 0, (5*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (-21*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (15*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1] diff --git a/besseltransforms/4-1-0.REMOVED.git-id b/besseltransforms/4-1-0.REMOVED.git-id new file mode 100644 index 0000000..f886e48 --- /dev/null +++ b/besseltransforms/4-1-0.REMOVED.git-id @@ -0,0 +1 @@ +bee84490a2f9b473adccfa023c6611be883a01a7 \ No newline at end of file diff --git a/besseltransforms/4-1-1 b/besseltransforms/4-1-1 deleted file mode 100644 index e162607..0000000 --- a/besseltransforms/4-1-1 +++ /dev/null @@ -1,2 +0,0 @@ -(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/4-1-1.REMOVED.git-id b/besseltransforms/4-1-1.REMOVED.git-id new file mode 100644 index 0000000..0bdd7c6 --- /dev/null +++ b/besseltransforms/4-1-1.REMOVED.git-id @@ -0,0 +1 @@ +a9ad81536da843935e33ae577308937e51c35ca7 \ No newline at end of file diff --git a/besseltransforms/4-1-2 b/besseltransforms/4-1-2 deleted file mode 100644 index f6793b6..0000000 --- a/besseltransforms/4-1-2 +++ /dev/null @@ -1,2 +0,0 @@ -(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/4-1-2.REMOVED.git-id b/besseltransforms/4-1-2.REMOVED.git-id new file mode 100644 index 0000000..45ce22a --- /dev/null +++ b/besseltransforms/4-1-2.REMOVED.git-id @@ -0,0 +1 @@ +8640f89aa7c80f216e563672dd2763f2c7becbce \ No newline at end of file diff --git a/besseltransforms/4-2-0 b/besseltransforms/4-2-0 index d8121c9..788e5e7 100644 --- a/besseltransforms/4-2-0 +++ b/besseltransforms/4-2-0 @@ -1,9 +1 @@ -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}] +Integrate[(E^(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] diff --git a/besseltransforms/4-2-1 b/besseltransforms/4-2-1 index e69de29..c73799a 100644 --- a/besseltransforms/4-2-1 +++ b/besseltransforms/4-2-1 @@ -0,0 +1,2 @@ +((-4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2 +Piecewise[{{SeriesData[k, Infinity, {(-3*c^4)/k0^2, 0, (-45*c^4)/2 + (195*c^6)/(2*k0^2) - ((90*I)*c^5)/k0, 0, (6825*c^6)/4 - (25515*c^8)/(16*k0^2) + ((2625*I)*c^7)/k0 - (525*I)*c^5*k0 - (525*c^4*k0^2)/8, 0, (105*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((c*(c - I*k0)^3)/2 - (3*c*(2*c - I*k0)^3)/2 + (3*c*(3*c - I*k0)^3)/2 - (c*(4*c - I*k0)^3)/2 - I/2*(c - I*k0)^3*k0 + (3*I)/4*(2*c - I*k0)^3*k0 - I/2*(3*c - I*k0)^3*k0 + I/8*(4*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/4 + (3*c*(2*c - I*k0)^5)/4 - (3*c*(3*c - I*k0)^5)/4 + (c*(4*c - I*k0)^5)/4 + I/4*(c - I*k0)^5*k0 - (3*I)/8*(2*c - I*k0)^5*k0 + I/4*(3*c - I*k0)^5*k0 - I/16*(4*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/32 - (15*c*(2*c - I*k0)^7)/32 + (15*c*(3*c - I*k0)^7)/32 - (5*c*(4*c - I*k0)^7)/32 - (5*I)/32*(c - I*k0)^7*k0 + (15*I)/64*(2*c - I*k0)^7*k0 - (5*I)/32*(3*c - I*k0)^7*k0 + (5*I)/128*(4*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/64 + (21*c*(2*c - I*k0)^9)/64 - (21*c*(3*c - I*k0)^9)/64 + (7*c*(4*c - I*k0)^9)/64 + (7*I)/64*(c - I*k0)^9*k0 - (21*I)/128*(2*c - I*k0)^9*k0 + (7*I)/64*(3*c - I*k0)^9*k0 - (7*I)/256*(4*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/4-2-2 b/besseltransforms/4-2-2 index a457fb2..e78fb3f 100644 --- a/besseltransforms/4-2-2 +++ b/besseltransforms/4-2-2 @@ -1,2 +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] +(-k^2 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) +SeriesData[k, Infinity, {(30*c^5)/k0^2 - ((15*I)*c^4)/k0, 0, 315*c^5 - (525*c^7)/k0^2 + ((1365*I)/2*c^6)/k0 - (105*I)/2*c^4*k0, 0, (315*(370*c^9 - (729*I)*c^8*k0 - 600*c^7*k0^2 + (260*I)*c^6*k0^3 + 60*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 5, 11, 1] diff --git a/besseltransforms/4-3-0 b/besseltransforms/4-3-0 index 25f3059..c39b980 100644 --- a/besseltransforms/4-3-0 +++ b/besseltransforms/4-3-0 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/4-3-1 b/besseltransforms/4-3-1 index 537e02d..c39b980 100644 --- a/besseltransforms/4-3-1 +++ b/besseltransforms/4-3-1 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/4-3-2 b/besseltransforms/4-3-2 index e5a281e..592b772 100644 --- a/besseltransforms/4-3-2 +++ b/besseltransforms/4-3-2 @@ -1,2 +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] +(8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 12*k^2*(-3 + 2*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 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3) +SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-5*(13*c^6 - (12*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (105*I)*c^5 + (5103*c^8)/(16*k0^3) - ((525*I)*c^7)/k0^2 - (1365*c^6)/(4*k0) + (105*c^4*k0)/8, 0, (-15*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1] diff --git a/besseltransforms/5-1-0 b/besseltransforms/5-1-0 deleted file mode 100644 index f5c54c7..0000000 --- a/besseltransforms/5-1-0 +++ /dev/null @@ -1,2 +0,0 @@ -(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/5-1-0.REMOVED.git-id b/besseltransforms/5-1-0.REMOVED.git-id new file mode 100644 index 0000000..f2b0b13 --- /dev/null +++ b/besseltransforms/5-1-0.REMOVED.git-id @@ -0,0 +1 @@ +6b5039445ac40a8e4dde06ee71a446ec8c971871 \ No newline at end of file diff --git a/besseltransforms/5-1-1 b/besseltransforms/5-1-1 deleted file mode 100644 index e376b4c..0000000 --- a/besseltransforms/5-1-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-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/5-1-1.REMOVED.git-id b/besseltransforms/5-1-1.REMOVED.git-id new file mode 100644 index 0000000..4a3c8ee --- /dev/null +++ b/besseltransforms/5-1-1.REMOVED.git-id @@ -0,0 +1 @@ +f5594061661eec519d31142141692d67f7b41978 \ No newline at end of file diff --git a/besseltransforms/5-1-2 b/besseltransforms/5-1-2 deleted file mode 100644 index eb4edb0..0000000 --- a/besseltransforms/5-1-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-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/5-1-2.REMOVED.git-id b/besseltransforms/5-1-2.REMOVED.git-id new file mode 100644 index 0000000..67c9a9d --- /dev/null +++ b/besseltransforms/5-1-2.REMOVED.git-id @@ -0,0 +1 @@ +a1c5acb5509b38870c8f208e65cec91b86716900 \ No newline at end of file diff --git a/besseltransforms/5-2-0 b/besseltransforms/5-2-0 index 6e741c5..f3c61c3 100644 --- a/besseltransforms/5-2-0 +++ b/besseltransforms/5-2-0 @@ -1,9 +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] +Integrate[(E^(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] - -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}] + 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 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 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 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 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 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 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 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 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 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] 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] 2401245 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] 3675 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] 9 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] E Sqrt[--] 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] 418854310875 E Sin[-- - 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] 57972915 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] 59535 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] 75 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] 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] + 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 +Series[Integrate[(E^(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], {k, Infinity, 10}] diff --git a/besseltransforms/5-2-1 b/besseltransforms/5-2-1 index 888a040..53b8241 100644 --- a/besseltransforms/5-2-1 +++ b/besseltransforms/5-2-1 @@ -1,2 +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] +(-10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-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) - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) +Piecewise[{{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], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((5*c*(c - I*k0)^3)/8 - (5*c*(2*c - I*k0)^3)/2 + (15*c*(3*c - I*k0)^3)/4 - (5*c*(4*c - I*k0)^3)/2 + (5*c*(5*c - I*k0)^3)/8 - (5*I)/8*(c - I*k0)^3*k0 + (5*I)/4*(2*c - I*k0)^3*k0 - (5*I)/4*(3*c - I*k0)^3*k0 + (5*I)/8*(4*c - I*k0)^3*k0 - I/8*(5*c - I*k0)^3*k0)/k0^2, 0, ((-5*c*(c - I*k0)^5)/16 + (5*c*(2*c - I*k0)^5)/4 - (15*c*(3*c - I*k0)^5)/8 + (5*c*(4*c - I*k0)^5)/4 - (5*c*(5*c - I*k0)^5)/16 + (5*I)/16*(c - I*k0)^5*k0 - (5*I)/8*(2*c - I*k0)^5*k0 + (5*I)/8*(3*c - I*k0)^5*k0 - (5*I)/16*(4*c - I*k0)^5*k0 + I/16*(5*c - I*k0)^5*k0)/k0^2, 0, ((25*c*(c - I*k0)^7)/128 - (25*c*(2*c - I*k0)^7)/32 + (75*c*(3*c - I*k0)^7)/64 - (25*c*(4*c - I*k0)^7)/32 + (25*c*(5*c - I*k0)^7)/128 - (25*I)/128*(c - I*k0)^7*k0 + (25*I)/64*(2*c - I*k0)^7*k0 - (25*I)/64*(3*c - I*k0)^7*k0 + (25*I)/128*(4*c - I*k0)^7*k0 - (5*I)/128*(5*c - I*k0)^7*k0)/k0^2, 0, ((-35*c*(c - I*k0)^9)/256 + (35*c*(2*c - I*k0)^9)/64 - (105*c*(3*c - I*k0)^9)/128 + (35*c*(4*c - I*k0)^9)/64 - (35*c*(5*c - I*k0)^9)/256 + (35*I)/256*(c - I*k0)^9*k0 - (35*I)/128*(2*c - I*k0)^9*k0 + (35*I)/128*(3*c - I*k0)^9*k0 - (35*I)/256*(4*c - I*k0)^9*k0 + (7*I)/256*(5*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/5-2-2 b/besseltransforms/5-2-2 index cc4cb40..bad9bad 100644 --- a/besseltransforms/5-2-2 +++ b/besseltransforms/5-2-2 @@ -1,2 +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] +(-k^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*(-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 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*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] diff --git a/besseltransforms/5-3-0 b/besseltransforms/5-3-0 index 4795bb0..c39b980 100644 --- a/besseltransforms/5-3-0 +++ b/besseltransforms/5-3-0 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/5-3-1 b/besseltransforms/5-3-1 index 1c8226b..c39b980 100644 --- a/besseltransforms/5-3-1 +++ b/besseltransforms/5-3-1 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/5-3-2 b/besseltransforms/5-3-2 index 39fc95b..bd05e82 100644 --- a/besseltransforms/5-3-2 +++ b/besseltransforms/5-3-2 @@ -1,2 +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] +(10*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 20*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 20*k^2*(3 - 2*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 + 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 + 2*k^2*(3 - 2*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^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3) +SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(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*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/6-1-0 b/besseltransforms/6-1-0 deleted file mode 100644 index 2caaed1..0000000 --- a/besseltransforms/6-1-0 +++ /dev/null @@ -1,2 +0,0 @@ -(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/6-1-0.REMOVED.git-id b/besseltransforms/6-1-0.REMOVED.git-id new file mode 100644 index 0000000..730bd75 --- /dev/null +++ b/besseltransforms/6-1-0.REMOVED.git-id @@ -0,0 +1 @@ +0f102e90aa5931a6786417ff8dc4af328dd43035 \ No newline at end of file diff --git a/besseltransforms/6-1-1 b/besseltransforms/6-1-1 deleted file mode 100644 index 72999b9..0000000 --- a/besseltransforms/6-1-1 +++ /dev/null @@ -1,2 +0,0 @@ -(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/6-1-1.REMOVED.git-id b/besseltransforms/6-1-1.REMOVED.git-id new file mode 100644 index 0000000..7533791 --- /dev/null +++ b/besseltransforms/6-1-1.REMOVED.git-id @@ -0,0 +1 @@ +481803dc1d1b689b8e54b8e3f2965fa3f2ec3ac3 \ No newline at end of file diff --git a/besseltransforms/6-1-2 b/besseltransforms/6-1-2 deleted file mode 100644 index 8885d97..0000000 --- a/besseltransforms/6-1-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-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/6-1-2.REMOVED.git-id b/besseltransforms/6-1-2.REMOVED.git-id new file mode 100644 index 0000000..326f61c --- /dev/null +++ b/besseltransforms/6-1-2.REMOVED.git-id @@ -0,0 +1 @@ +9280f56d85a627d34557e5b7ee0692b99af6adf2 \ No newline at end of file diff --git a/besseltransforms/6-2-0 b/besseltransforms/6-2-0 index 4a3dea6..c39b980 100644 --- a/besseltransforms/6-2-0 +++ b/besseltransforms/6-2-0 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/6-2-1 b/besseltransforms/6-2-1 index a042203..5293800 100644 --- a/besseltransforms/6-2-1 +++ b/besseltransforms/6-2-1 @@ -1,2 +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] +(-12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 30*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 30*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 12*(-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) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) +Piecewise[{{SeriesData[k, Infinity, {(45*c^6)/k0^2, 0, (1575*c^6)/2 - (29925*c^8)/(4*k0^2) + ((4725*I)*c^7)/k0, 0, (6615*(1087*c^10 - (1260*I)*c^9*k0 - 570*c^8*k0^2 + (120*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^2)}, 6, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/4 - (15*c*(2*c - I*k0)^3)/4 + (15*c*(3*c - I*k0)^3)/2 - (15*c*(4*c - I*k0)^3)/2 + (15*c*(5*c - I*k0)^3)/4 - (3*c*(6*c - I*k0)^3)/4 - (3*I)/4*(c - I*k0)^3*k0 + (15*I)/8*(2*c - I*k0)^3*k0 - (5*I)/2*(3*c - I*k0)^3*k0 + (15*I)/8*(4*c - I*k0)^3*k0 - (3*I)/4*(5*c - I*k0)^3*k0 + I/8*(6*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/8 + (15*c*(2*c - I*k0)^5)/8 - (15*c*(3*c - I*k0)^5)/4 + (15*c*(4*c - I*k0)^5)/4 - (15*c*(5*c - I*k0)^5)/8 + (3*c*(6*c - I*k0)^5)/8 + (3*I)/8*(c - I*k0)^5*k0 - (15*I)/16*(2*c - I*k0)^5*k0 + (5*I)/4*(3*c - I*k0)^5*k0 - (15*I)/16*(4*c - I*k0)^5*k0 + (3*I)/8*(5*c - I*k0)^5*k0 - I/16*(6*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/64 - (75*c*(2*c - I*k0)^7)/64 + (75*c*(3*c - I*k0)^7)/32 - (75*c*(4*c - I*k0)^7)/32 + (75*c*(5*c - I*k0)^7)/64 - (15*c*(6*c - I*k0)^7)/64 - (15*I)/64*(c - I*k0)^7*k0 + (75*I)/128*(2*c - I*k0)^7*k0 - (25*I)/32*(3*c - I*k0)^7*k0 + (75*I)/128*(4*c - I*k0)^7*k0 - (15*I)/64*(5*c - I*k0)^7*k0 + (5*I)/128*(6*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/128 + (105*c*(2*c - I*k0)^9)/128 - (105*c*(3*c - I*k0)^9)/64 + (105*c*(4*c - I*k0)^9)/64 - (105*c*(5*c - I*k0)^9)/128 + (21*c*(6*c - I*k0)^9)/128 + (21*I)/128*(c - I*k0)^9*k0 - (105*I)/256*(2*c - I*k0)^9*k0 + (35*I)/64*(3*c - I*k0)^9*k0 - (105*I)/256*(4*c - I*k0)^9*k0 + (21*I)/128*(5*c - I*k0)^9*k0 - (7*I)/256*(6*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/6-2-2 b/besseltransforms/6-2-2 index dd9197e..4f80592 100644 --- a/besseltransforms/6-2-2 +++ b/besseltransforms/6-2-2 @@ -1,2 +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] +(-k^2 + 12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 30*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 30*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) +SeriesData[k, Infinity, {(-945*c^7)/k0^2 + ((315*I)*c^6)/k0, 0, (4725*(63*c^9 - (57*I)*c^8*k0 - 18*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/6-3-0 b/besseltransforms/6-3-0 index b942fa3..c39b980 100644 --- a/besseltransforms/6-3-0 +++ b/besseltransforms/6-3-0 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/6-3-1 b/besseltransforms/6-3-1 index daed903..c39b980 100644 --- a/besseltransforms/6-3-1 +++ b/besseltransforms/6-3-1 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/6-3-2 b/besseltransforms/6-3-2 index ccb328f..d31d17d 100644 --- a/besseltransforms/6-3-2 +++ b/besseltransforms/6-3-2 @@ -1,2 +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] +((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 + (5*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/2 + (5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + (10*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/3 - (20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2) + (5*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/2 + (5*(-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)/k^2 + ((-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) + (k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/4)/k0^3 +SeriesData[k, Infinity, {(-15*c^6)/k0^3, 0, (315*(19*c^8 - (12*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-945*(1087*c^10 - (1260*I)*c^9*k0 - 570*c^8*k0^2 + (120*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^3)}, 5, 11, 1] diff --git a/besseltransforms/7-1-0 b/besseltransforms/7-1-0 deleted file mode 100644 index 83e622d..0000000 --- a/besseltransforms/7-1-0 +++ /dev/null @@ -1,2 +0,0 @@ -(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/7-1-0.REMOVED.git-id b/besseltransforms/7-1-0.REMOVED.git-id new file mode 100644 index 0000000..ac74957 --- /dev/null +++ b/besseltransforms/7-1-0.REMOVED.git-id @@ -0,0 +1 @@ +ae505b9d4c1eeaa06af2c14fbf57097d2e776630 \ No newline at end of file diff --git a/besseltransforms/7-1-1 b/besseltransforms/7-1-1 deleted file mode 100644 index 619fe49..0000000 --- a/besseltransforms/7-1-1 +++ /dev/null @@ -1,2 +0,0 @@ -(-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/7-1-1.REMOVED.git-id b/besseltransforms/7-1-1.REMOVED.git-id new file mode 100644 index 0000000..a28c3cd --- /dev/null +++ b/besseltransforms/7-1-1.REMOVED.git-id @@ -0,0 +1 @@ +2ba9a09f1db5bc6a45dd3b7edebf70f39529b350 \ No newline at end of file diff --git a/besseltransforms/7-1-2 b/besseltransforms/7-1-2 deleted file mode 100644 index a4632ba..0000000 --- a/besseltransforms/7-1-2 +++ /dev/null @@ -1,2 +0,0 @@ -(-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/7-1-2.REMOVED.git-id b/besseltransforms/7-1-2.REMOVED.git-id new file mode 100644 index 0000000..5b7552f --- /dev/null +++ b/besseltransforms/7-1-2.REMOVED.git-id @@ -0,0 +1 @@ +ffac63299c303e912d85a312d47d1b59b898daf7 \ No newline at end of file diff --git a/besseltransforms/7-2-0 b/besseltransforms/7-2-0 index d8314d1..c39b980 100644 --- a/besseltransforms/7-2-0 +++ b/besseltransforms/7-2-0 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/7-2-1 b/besseltransforms/7-2-1 index 3ba0bd1..f4300bc 100644 --- a/besseltransforms/7-2-1 +++ b/besseltransforms/7-2-1 @@ -1,2 +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] +(-14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 14*(-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) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2) +Piecewise[{{SeriesData[k, Infinity, {(11025*c^8)/(2*k0^2) - ((1575*I)*c^7)/k0, 0, (-33075*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((7*c*(c - I*k0)^3)/8 - (21*c*(2*c - I*k0)^3)/4 + (105*c*(3*c - I*k0)^3)/8 - (35*c*(4*c - I*k0)^3)/2 + (105*c*(5*c - I*k0)^3)/8 - (21*c*(6*c - I*k0)^3)/4 + (7*c*(7*c - I*k0)^3)/8 - (7*I)/8*(c - I*k0)^3*k0 + (21*I)/8*(2*c - I*k0)^3*k0 - (35*I)/8*(3*c - I*k0)^3*k0 + (35*I)/8*(4*c - I*k0)^3*k0 - (21*I)/8*(5*c - I*k0)^3*k0 + (7*I)/8*(6*c - I*k0)^3*k0 - I/8*(7*c - I*k0)^3*k0)/k0^2, 0, ((-7*c*(c - I*k0)^5)/16 + (21*c*(2*c - I*k0)^5)/8 - (105*c*(3*c - I*k0)^5)/16 + (35*c*(4*c - I*k0)^5)/4 - (105*c*(5*c - I*k0)^5)/16 + (21*c*(6*c - I*k0)^5)/8 - (7*c*(7*c - I*k0)^5)/16 + (7*I)/16*(c - I*k0)^5*k0 - (21*I)/16*(2*c - I*k0)^5*k0 + (35*I)/16*(3*c - I*k0)^5*k0 - (35*I)/16*(4*c - I*k0)^5*k0 + (21*I)/16*(5*c - I*k0)^5*k0 - (7*I)/16*(6*c - I*k0)^5*k0 + I/16*(7*c - I*k0)^5*k0)/k0^2, 0, ((35*c*(c - I*k0)^7)/128 - (105*c*(2*c - I*k0)^7)/64 + (525*c*(3*c - I*k0)^7)/128 - (175*c*(4*c - I*k0)^7)/32 + (525*c*(5*c - I*k0)^7)/128 - (105*c*(6*c - I*k0)^7)/64 + (35*c*(7*c - I*k0)^7)/128 - (35*I)/128*(c - I*k0)^7*k0 + (105*I)/128*(2*c - I*k0)^7*k0 - (175*I)/128*(3*c - I*k0)^7*k0 + (175*I)/128*(4*c - I*k0)^7*k0 - (105*I)/128*(5*c - I*k0)^7*k0 + (35*I)/128*(6*c - I*k0)^7*k0 - (5*I)/128*(7*c - I*k0)^7*k0)/k0^2, 0, ((-49*c*(c - I*k0)^9)/256 + (147*c*(2*c - I*k0)^9)/128 - (735*c*(3*c - I*k0)^9)/256 + (245*c*(4*c - I*k0)^9)/64 - (735*c*(5*c - I*k0)^9)/256 + (147*c*(6*c - I*k0)^9)/128 - (49*c*(7*c - I*k0)^9)/256 + (49*I)/256*(c - I*k0)^9*k0 - (147*I)/256*(2*c - I*k0)^9*k0 + (245*I)/256*(3*c - I*k0)^9*k0 - (245*I)/256*(4*c - I*k0)^9*k0 + (147*I)/256*(5*c - I*k0)^9*k0 - (49*I)/256*(6*c - I*k0)^9*k0 + (7*I)/256*(7*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]] diff --git a/besseltransforms/7-2-2 b/besseltransforms/7-2-2 index 743a6ce..ee8e04c 100644 --- a/besseltransforms/7-2-2 +++ b/besseltransforms/7-2-2 @@ -1,2 +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] +(-k^2 + 14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 14*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2) +SeriesData[k, Infinity, {(315*c^7)/k0^2, 0, (-4725*(77*c^9 - (42*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] diff --git a/besseltransforms/7-3-0 b/besseltransforms/7-3-0 index 854eabc..c39b980 100644 --- a/besseltransforms/7-3-0 +++ b/besseltransforms/7-3-0 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/7-3-1 b/besseltransforms/7-3-1 index 54b7244..c39b980 100644 --- a/besseltransforms/7-3-1 +++ b/besseltransforms/7-3-1 @@ -1,9 +1,2 @@ -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}] +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/7-3-2 b/besseltransforms/7-3-2 index 74b61aa..7e0c894 100644 --- a/besseltransforms/7-3-2 +++ b/besseltransforms/7-3-2 @@ -1,2 +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] +(14*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 28*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 42*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 84*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 70*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 140*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 70*k^2*(-3 + 2*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 + 42*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 84*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 14*k^2*(-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 28*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 2*k^2*(3 - 2*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^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3) +SeriesData[k, Infinity, {(-2205*c^8)/(2*k0^3) + ((315*I)*c^7)/k0^2, 0, (4725*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1] diff --git a/besseltransforms/klarge/5-3-0 b/besseltransforms/klarge/5-3-0 index 131b3d3..24dbc15 100644 --- a/besseltransforms/klarge/5-3-0 +++ b/besseltransforms/klarge/5-3-0 @@ -1,13 +1,11 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 2401245 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] 3675 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] 9 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] E Sqrt[--] 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] 418854310875 E Sin[-- - 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] 57972915 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] 59535 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] 75 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] 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + -5 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 3 23/2 + 8589934592 k k0 Sqrt[2 Pi] x Series[Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. Integrate[(E^(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] diff --git a/besseltransforms/klarge/5-3-1 b/besseltransforms/klarge/5-3-1 index 7a72648..f14813c 100644 --- a/besseltransforms/klarge/5-3-1 +++ b/besseltransforms/klarge/5-3-1 @@ -8,6 +8,4 @@ Integrate::idiv: Integral of ------------------------------------- - ----------- 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 Series[Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. Integrate[(E^(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] diff --git a/besseltransforms/klarge/5-4-0 b/besseltransforms/klarge/5-4-0 index 6061ee1..d82c8a2 100644 --- a/besseltransforms/klarge/5-4-0 +++ b/besseltransforms/klarge/5-4-0 @@ -1,13 +1,11 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 2401245 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] 3675 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] 9 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] E Sqrt[--] 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] 418854310875 E Sin[-- - 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] 57972915 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] 59535 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] 75 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] 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + -5 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^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] - -Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. Integrate[(E^(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] diff --git a/besseltransforms/klarge/5-4-1 b/besseltransforms/klarge/5-4-1 index f119151..bcb3949 100644 --- a/besseltransforms/klarge/5-4-1 +++ b/besseltransforms/klarge/5-4-1 @@ -1,11 +1,11 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 2837835 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] 4725 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] 15 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] E Sqrt[--] 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] 468131288625 E Sin[-- + 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] 66891825 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] 72765 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] 105 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] 3 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + -5 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 4 25/2 + 8589934592 k k0 Sqrt[2 Pi] x Series[Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Integrate[(E^(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] diff --git a/besseltransforms/klarge/5-5-0 b/besseltransforms/klarge/5-5-0 index 506247d..467046e 100644 --- a/besseltransforms/klarge/5-5-0 +++ b/besseltransforms/klarge/5-5-0 @@ -1,11 +1,13 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 2401245 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] 3675 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] 9 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] E Sqrt[--] 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] 418854310875 E Sin[-- - 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] 57972915 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] 59535 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] 75 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] 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + -5 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 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x Series[Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] + +Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. Integrate[(E^(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] diff --git a/besseltransforms/klarge/5-5-1 b/besseltransforms/klarge/5-5-1 index 694c83a..3f93e32 100644 --- a/besseltransforms/klarge/5-5-1 +++ b/besseltransforms/klarge/5-5-1 @@ -1,12 +1,12 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 2837835 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] 4725 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] 15 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] E Sqrt[--] 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] 468131288625 E Sin[-- + 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] 66891825 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] 72765 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] 105 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] 3 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + -5 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 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x Series[Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. diff --git a/besseltransforms/klarge/5-5-2 b/besseltransforms/klarge/5-5-2 index d2b30c2..434adf3 100644 --- a/besseltransforms/klarge/5-5-2 +++ b/besseltransforms/klarge/5-5-2 @@ -1,11 +1,11 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 4729725 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] 10395 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] 105 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] E Sqrt[--] 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] 655383804075 E Sin[-- - 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] 103378275 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] 135135 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] 315 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] 15 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + -5 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 5 27/2 + 8589934592 k k0 Sqrt[2 Pi] x Series[Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Integrate[(E^(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] diff --git a/besseltransforms/klarge/5-5-3 b/besseltransforms/klarge/5-5-3 index ecdb0d3..e64b420 100644 --- a/besseltransforms/klarge/5-5-3 +++ b/besseltransforms/klarge/5-5-3 @@ -1,12 +1,13 @@ Integrate[(E^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(3,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) - 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 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 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 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 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 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 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 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 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 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] 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] 11486475 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] 45045 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] 945 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] E Sqrt[--] 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] 1159525191825 E Sin[-- + 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] 218243025 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] 405405 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] 3465 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] 35 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] - 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 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 2097152 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 16384 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 64 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 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 4294967296 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 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 131072 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 512 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 4 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 + 2 2 4 4 6 6 8 8 + -5 c x + I k0 x c x 5 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^(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 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.