Bessel transform mathematica results etc.

Former-commit-id: 3dca9d0ccbfefa4c5f3867ce4ba31229646ca2d9

besseltransforms/2-1-0

@@ -0,0 +1,2 @@
+(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 2/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/k0
+SeriesData[k, Infinity, {-(c^2/(k*k0)), 0, (3*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (-5*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (35*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k*k0), 0, (-63*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1]

besseltransforms/2-1-1

@@ -0,0 +1,2 @@
+-((-2 + 2*(1 - 1/Sqrt[1 + k^2/(2*c - I*k0)^2]) + 1/Sqrt[1 + k^2/(c - I*k0)^2] + 1/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k*k0))
+SeriesData[k, Infinity, {(3*(2*c^3 - I*c^2*k0))/(k*k0), 0, (-15*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (35*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k*k0), 0, (-105*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 3, 11, 1]

besseltransforms/2-1-2

@@ -0,0 +1,2 @@
+(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 2/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (6*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (-6*c + (2*I)*k0)/k^2 + (8*c - (4*I)*k0)/k^2 + (-8*c + (4*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(3*c^2)/(k*k0), 0, (-5*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (-45*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k*k0), 0, (77*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1]

besseltransforms/2-1-3

@@ -0,0 +1,2 @@
+((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^3*k0)
+SeriesData[k, Infinity, {(8*c^2)/(k*k0), (-15*(2*c^3 - I*c^2*k0))/(k*k0), 0, (35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (63*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (165*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1]

besseltransforms/2-1-4

@@ -0,0 +1,2 @@
+((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^4*k0)
+SeriesData[k, Infinity, {(15*c^2)/(k*k0), (-48*(2*c^3 - I*c^2*k0))/(k*k0), (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), 0, (-21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (-99*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (-143*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1]

besseltransforms/2-1-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^5*k0)
+SeriesData[k, Infinity, {(24*c^2)/(k*k0), (-105*(2*c^3 - I*c^2*k0))/(k*k0), (32*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), 0, (231*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k*k0), 0, (429*(-3110*c^9 + (9075*I)*c^8*k0 + 11592*c^7*k0^2 - (8428*I)*c^6*k0^3 - 3780*c^5*k0^4 + (1050*I)*c^4*k0^5 + 168*c^3*k0^6 - (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1]

besseltransforms/2-1-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)))/(k^6*k0)
+SeriesData[k, Infinity, {(35*c^2)/(k*k0), (-192*(2*c^3 - I*c^2*k0))/(k*k0), (315*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k*k0), (-320*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(k*k0), (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k*k0), 0, (429*(-3025*c^8 + (7728*I)*c^7*k0 + 8428*c^6*k0^2 - (5040*I)*c^5*k0^3 - 1750*c^4*k0^4 + (336*I)*c^3*k0^5 + 28*c^2*k0^6))/(64*k*k0), 0, (429*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k*k0)}, 2, 11, 1]

besseltransforms/2-1-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/Sqrt[1 + k^2/(c - I*k0)^2] - (2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/Sqrt[1 + k^2/(2*c - I*k0)^2] + (k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/Sqrt[1 + k^2/(3*c - I*k0)^2])/(k^7*k0)
+SeriesData[k, Infinity, {(48*c^2)/(k*k0), (-315*(2*c^3 - I*c^2*k0))/(k*k0), (160*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(k*k0), (-3465*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k*k0), (128*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(k*k0), (3003*(-138*c^7 + (301*I)*c^6*k0 + 270*c^5*k0^2 - (125*I)*c^4*k0^3 - 30*c^3*k0^4 + (3*I)*c^2*k0^5))/(8*k*k0), 0, (2145*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k*k0)}, 2, 11, 1]

besseltransforms/2-2-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -3 c x + I k0 x        c x 2                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   2             21/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/2-2-1

@@ -0,0 +1,2 @@
+((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/(k*k0^2)
+SeriesData[k, Infinity, {c^2/k0^2, 0, (3*c^2)/2 - (25*c^4)/(4*k0^2) + ((6*I)*c^3)/k0, 0, (301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4)/(8*k0^2), 0, (-5*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (7*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1]

besseltransforms/2-2-2

@@ -0,0 +1,2 @@
+-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/(k^2*k0^2))
+SeriesData[k, Infinity, {(2*c^2)/k0^2, (-6*c^3)/k0^2 + ((3*I)*c^2)/k0, 0, -15*c^3 + (45*c^5)/(2*k0^2) - ((125*I)/4*c^4)/k0 + (5*I)/2*c^2*k0, 0, (-7*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (15*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1]

besseltransforms/2-2-3

@@ -0,0 +1,2 @@
+(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 2*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^3*k0^2)
+SeriesData[k, Infinity, {(3*c^2)/k0^2, (-16*c^3)/k0^2 + ((8*I)*c^2)/k0, (-15*c^2)/2 + (125*c^4)/(4*k0^2) - ((30*I)*c^3)/k0, 0, (-7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^2), 0, (9*(3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (-11*(28501*c^10 - (93300*I)*c^9*k0 - 136125*c^8*k0^2 + (115920*I)*c^7*k0^3 + 63210*c^6*k0^4 - (22680*I)*c^5*k0^5 - 5250*c^4*k0^6 + (720*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1]

besseltransforms/2-2-4

@@ -0,0 +1,2 @@
+-(2*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 2*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(2*k^4*k0^2)
+SeriesData[k, Infinity, {(4*c^2)/k0^2, (-30*c^3)/k0^2 + ((15*I)*c^2)/k0, -24*c^2 + (100*c^4)/k0^2 - ((96*I)*c^3)/k0, 105*c^3 - (315*c^5)/(2*k0^2) + ((875*I)/4*c^4)/k0 - (35*I)/2*c^2*k0, 0, (21*(138*c^7 - (301*I)*c^6*k0 - 270*c^5*k0^2 + (125*I)*c^4*k0^3 + 30*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (-33*(3110*c^9 - (9075*I)*c^8*k0 - 11592*c^7*k0^2 + (8428*I)*c^6*k0^3 + 3780*c^5*k0^4 - (1050*I)*c^4*k0^5 - 168*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1]

besseltransforms/2-2-5

@@ -0,0 +1,2 @@
+(-2*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(5*k^5*k0^2)
+SeriesData[k, Infinity, {(5*c^2)/k0^2, (-24*(2*c^3 - I*c^2*k0))/k0^2, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-32*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), 0, ((-165*(c - I*k0)^8)/128 + (165*(2*c - I*k0)^8)/64 - (165*(3*c - I*k0)^8)/128)/(5*k0^2), 0, ((143*(c - I*k0)^10)/256 - (143*(2*c - I*k0)^10)/128 + (143*(3*c - I*k0)^10)/256)/(5*k0^2)}, 2, 11, 1]

besseltransforms/2-2-6

@@ -0,0 +1,2 @@
+(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(3*k^6*k0^2)
+SeriesData[k, Infinity, {(6*c^2)/k0^2, (-35*(2*c^3 - I*c^2*k0))/k0^2, (16*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^2, (-315*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), (16*(c - I*k0)^6 - 32*(2*c - I*k0)^6 + 16*(3*c - I*k0)^6)/(3*k0^2), ((-99*(c - I*k0)^7)/16 + (99*(2*c - I*k0)^7)/8 - (99*(3*c - I*k0)^7)/16)/(3*k0^2), 0, ((143*(c - I*k0)^9)/128 - (143*(2*c - I*k0)^9)/64 + (143*(3*c - I*k0)^9)/128)/(3*k0^2)}, 2, 11, 1]

besseltransforms/2-2-7

@@ -0,0 +1,2 @@
+(-2*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(7*k^7*k0^2)
+SeriesData[k, Infinity, {(7*c^2)/k0^2, (-48*(2*c^3 - I*c^2*k0))/k0^2, (105*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^2), (-160*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^2, (231*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^2), (-64*(c - I*k0)^7 + 128*(2*c - I*k0)^7 - 64*(3*c - I*k0)^7)/(7*k0^2), ((3003*(c - I*k0)^8)/128 - (3003*(2*c - I*k0)^8)/64 + (3003*(3*c - I*k0)^8)/128)/(7*k0^2), 0, ((-1001*(c - I*k0)^10)/256 + (1001*(2*c - I*k0)^10)/128 - (1001*(3*c - I*k0)^10)/256)/(7*k0^2)}, 2, 11, 1]

besseltransforms/2-3-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -3 c x + I k0 x        c x 2                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   3             23/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/2-3-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -3 c x + I k0 x        c x 2                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   3             23/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^2*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 2 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/2-3-2

@@ -0,0 +1,2 @@
+((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 - 2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - (4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + (-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2)/(6*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-4*c^3)/k0^3 + ((2*I)*c^2)/k0^2, (25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2)/(4*k0^3), 0, (-301*c^6 + (540*I)*c^5*k0 + 375*c^4*k0^2 - (120*I)*c^3*k0^3 - 15*c^2*k0^4)/(24*k0^3), 0, (3025*c^8 - (7728*I)*c^7*k0 - 8428*c^6*k0^2 + (5040*I)*c^5*k0^3 + 1750*c^4*k0^4 - (336*I)*c^3*k0^5 - 28*c^2*k0^6)/(64*k0^3), 0, (-28501*c^10 + (93300*I)*c^9*k0 + 136125*c^8*k0^2 - (115920*I)*c^7*k0^3 - 63210*c^6*k0^4 + (22680*I)*c^5*k0^5 + 5250*c^4*k0^6 - (720*I)*c^3*k0^7 - 45*c^2*k0^8)/(128*k0^3)}, 1, 11, 1]

besseltransforms/2-3-3

@@ -0,0 +1,2 @@
+(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4)/(6*k^3*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-3*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(3*k0^3), (-5*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), 0, ((c - I*k0)^7/8 - (2*c - I*k0)^7/4 + (3*c - I*k0)^7/8)/(6*k0^3), 0, ((-3*(c - I*k0)^9)/64 + (3*(2*c - I*k0)^9)/32 - (3*(3*c - I*k0)^9)/64)/(6*k0^3), 0, ((3*(c - I*k0)^11)/128 - (3*(2*c - I*k0)^11)/64 + (3*(3*c - I*k0)^11)/128)/(6*k0^3)}, 1, 11, 1]

besseltransforms/2-3-4

@@ -0,0 +1,2 @@
+(-2*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(60*k^4*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-4*(2*c^3 - I*c^2*k0))/k0^3, (5*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(4*k0^3), (-4*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (7*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(24*k0^3), 0, ((-45*(c - I*k0)^8)/32 + (45*(2*c - I*k0)^8)/16 - (45*(3*c - I*k0)^8)/32)/(60*k0^3), 0, ((33*(c - I*k0)^10)/64 - (33*(2*c - I*k0)^10)/32 + (33*(3*c - I*k0)^10)/64)/(60*k0^3)}, 1, 11, 1]

besseltransforms/2-3-5

@@ -0,0 +1,2 @@
+(6*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 6*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 4*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(60*k^5*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-5*(2*c^3 - I*c^2*k0))/k0^3, (2*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-35*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (32*(c - I*k0)^6 - 64*(2*c - I*k0)^6 + 32*(3*c - I*k0)^6)/(60*k0^3), ((-45*(c - I*k0)^7)/4 + (45*(2*c - I*k0)^7)/2 - (45*(3*c - I*k0)^7)/4)/(60*k0^3), 0, ((55*(c - I*k0)^9)/32 - (55*(2*c - I*k0)^9)/16 + (55*(3*c - I*k0)^9)/32)/(60*k0^3), 0, ((-39*(c - I*k0)^11)/64 + (39*(2*c - I*k0)^11)/32 - (39*(3*c - I*k0)^11)/64)/(60*k0^3)}, 1, 11, 1]

besseltransforms/2-3-6

@@ -0,0 +1,2 @@
+(-2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(210*k^6*k0^3)
+SeriesData[k, Infinity, {c^2/k0^3, (-6*(2*c^3 - I*c^2*k0))/k0^3, (35*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/(12*k0^3), (-16*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/k0^3, (21*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k0^3), (-160*(c - I*k0)^7 + 320*(2*c - I*k0)^7 - 160*(3*c - I*k0)^7)/(210*k0^3), ((3465*(c - I*k0)^8)/64 - (3465*(2*c - I*k0)^8)/32 + (3465*(3*c - I*k0)^8)/64)/(210*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (1001*(2*c - I*k0)^10)/64 - (1001*(3*c - I*k0)^10)/128)/(210*k0^3)}, 1, 11, 1]

besseltransforms/2-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(168*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {c^2/k0^3, (-7*(2*c^3 - I*c^2*k0))/k0^3, (4*(25*c^4 - (24*I)*c^3*k0 - 6*c^2*k0^2))/k0^3, (-105*(18*c^5 - (25*I)*c^4*k0 - 12*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^3), (16*(301*c^6 - (540*I)*c^5*k0 - 375*c^4*k0^2 + (120*I)*c^3*k0^3 + 15*c^2*k0^4))/(3*k0^3), ((-33*(c - I*k0)^7)/16 + (33*(2*c - I*k0)^7)/8 - (33*(3*c - I*k0)^7)/16)/k0^3, ((8*(c - I*k0)^8)/7 - (16*(2*c - I*k0)^8)/7 + (8*(3*c - I*k0)^8)/7)/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/192 - (143*(3*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (13*(2*c - I*k0)^11)/128 + (13*(3*c - I*k0)^11)/256)/k0^3}, 1, 11, 1]

besseltransforms/3-2-1

@@ -0,0 +1,2 @@
+((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 3*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 3*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/(k*k0^2)
+SeriesData[k, Infinity, {(15*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^2), 0, (-105*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^2)}, 4, 11, 1]

besseltransforms/3-3-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -4 c x + I k0 x        c x 3                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   3             23/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/3-3-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -4 c x + I k0 x        c x 3                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   3             23/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^3*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 3 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/3-3-2

@@ -0,0 +1,2 @@
+((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 3*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 3*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + (6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2)/(6*k0^3)
+SeriesData[k, Infinity, {(2*c^3)/k0^3, (-15*c^4)/(2*k0^3) + ((3*I)*c^3)/k0^2, 0, (5*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (-21*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (15*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1]

besseltransforms/3-3-3

@@ -0,0 +1,2 @@
+(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 3*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 3*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4)/(6*k^3*k0^3)
+SeriesData[k, Infinity, {(3*c^3)/k0^3, (-20*c^4)/k0^3 + ((8*I)*c^3)/k0^2, (15*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), 0, (-7*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (3*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, (-33*(55591*c^11 - (145750*I)*c^10*k0 - 170525*c^9*k0^2 + (116550*I)*c^8*k0^3 + 51030*c^7*k0^4 - (14700*I)*c^6*k0^5 - 2730*c^5*k0^6 + (300*I)*c^4*k0^7 + 15*c^3*k0^8))/(128*k0^3)}, 2, 11, 1]

besseltransforms/3-3-4

@@ -0,0 +1,2 @@
+(-3*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 3*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 - k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(60*k^4*k0^3)
+SeriesData[k, Infinity, {(4*c^3)/k0^3, (-75*c^4)/(2*k0^3) + ((15*I)*c^3)/k0^2, (156*c^5)/k0^3 - ((120*I)*c^4)/k0^2 - (24*c^3)/k0, (-35*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (63*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (-33*(14575*c^10 - (34105*I)*c^9*k0 - 34965*c^8*k0^2 + (20412*I)*c^7*k0^3 + 7350*c^6*k0^4 - (1638*I)*c^5*k0^5 - 210*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1]

besseltransforms/3-3-5

@@ -0,0 +1,2 @@
+(3*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 9*k^4*(-5 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*k^2*(-15 + 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 48*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 + 9*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 6*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 48*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 3*k^4*(-5 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*k^2*(-15 + 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5*k0^3)
+SeriesData[k, Infinity, {(5*c^3)/k0^3, (-12*(5*c^4 - (2*I)*c^3*k0))/k0^3, (105*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-32*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (63*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), 0, (-11*(34105*c^9 - (69930*I)*c^8*k0 - 61236*c^7*k0^2 + (29400*I)*c^6*k0^3 + 8190*c^5*k0^4 - (1260*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^3), 0, ((-39*(c - I*k0)^11)/128 + (117*(2*c - I*k0)^11)/128 - (117*(3*c - I*k0)^11)/128 + (39*(4*c - I*k0)^11)/128)/(30*k0^3)}, 2, 11, 1]

besseltransforms/3-3-6

@@ -0,0 +1,2 @@
+(-3*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 3*(k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) + k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 - k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 - 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 - 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^6*k0^3)
+SeriesData[k, Infinity, {(6*c^3)/k0^3, (-35*(5*c^4 - (2*I)*c^3*k0))/(2*k0^3), (48*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/k0^3, (-315*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), (32*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/k0^3, (-693*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, ((-1001*(c - I*k0)^10)/128 + (3003*(2*c - I*k0)^10)/128 - (3003*(3*c - I*k0)^10)/128 + (1001*(4*c - I*k0)^10)/128)/(210*k0^3)}, 2, 11, 1]

besseltransforms/3-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(112*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(112*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {(7*c^3)/k0^3, (-24*(5*c^4 - (2*I)*c^3*k0))/k0^3, (315*(13*c^5 - (10*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^3), (-160*(35*c^6 - (39*I)*c^5*k0 - 15*c^4*k0^2 + (2*I)*c^3*k0^3))/k0^3, (693*(243*c^7 - (350*I)*c^6*k0 - 195*c^5*k0^2 + (50*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^3), (-96*(555*c^8 - (972*I)*c^7*k0 - 700*c^6*k0^2 + (260*I)*c^5*k0^3 + 50*c^4*k0^4 - (4*I)*c^3*k0^5))/k0^3, ((-143*(c - I*k0)^9)/384 + (143*(2*c - I*k0)^9)/128 - (143*(3*c - I*k0)^9)/128 + (143*(4*c - I*k0)^9)/384)/k0^3, 0, ((13*(c - I*k0)^11)/256 - (39*(2*c - I*k0)^11)/256 + (39*(3*c - I*k0)^11)/256 - (13*(4*c - I*k0)^11)/256)/k0^3}, 2, 11, 1]

besseltransforms/4-1-1

@@ -0,0 +1,2 @@
+(2/k - 4*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 6*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 4*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {((45*I)*c^4)/k - (135*c^5)/(k*k0), 0, (525*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (-2205*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 5, 11, 1]

besseltransforms/4-1-2

@@ -0,0 +1,2 @@
+(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 4/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 6/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (12*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) - 4/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (-10*c + (2*I)*k0)/k^2 + (16*c - (8*I)*k0)/k^2 + (32*c - (8*I)*k0)/k^2 + (-32*c + (8*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-16*c + (8*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-36*c + (12*I)*k0)/k^2)/k0
+SeriesData[k, Infinity, {(-15*c^4)/(k*k0), 0, (105*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (-945*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (1155*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1]

besseltransforms/4-1-3

@@ -0,0 +1,2 @@
+((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {((-105*I)*c^4)/k + (315*c^5)/(k*k0), 0, (-945*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (3465*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 5, 11, 1]

besseltransforms/4-1-4

@@ -0,0 +1,2 @@
+((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0
+SeriesData[k, Infinity, {(105*c^4)/(k*k0), 0, (-315*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (2079*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1]

besseltransforms/4-1-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(384*c^4)/(k*k0), ((945*I)*c^4)/k - (2835*c^5)/(k*k0), 0, (3465*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (-9009*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1]

besseltransforms/4-1-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (6*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (4*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)))/k0
+SeriesData[k, Infinity, {(945*c^4)/(k*k0), ((3840*I)*c^4)/k - (11520*c^5)/(k*k0), (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k*k0), 0, (-9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k*k0), 0, (6435*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k*k0)}, 4, 11, 1]

besseltransforms/4-1-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(1920*c^4)/(k*k0), ((10395*I)*c^4)/k - (31185*c^5)/(k*k0), (7680*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(k*k0), (-45045*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k*k0), 0, (45045*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k*k0)}, 4, 11, 1]

besseltransforms/4-2-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -5 c x + I k0 x        c x 4                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   2             21/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-2-2

@@ -0,0 +1,2 @@
+-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^2*k0^2))
+SeriesData[k, Infinity, {(45*c^5)/k0^2 - ((15*I)*c^4)/k0, 0, (945*c^5)/2 - (1575*c^7)/k0^2 + ((1470*I)*c^6)/k0 - (105*I)/2*c^4*k0, 0, (315*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 5, 11, 1]

besseltransforms/4-2-3

@@ -0,0 +1,2 @@
+(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 4*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^3*k0^2)
+SeriesData[k, Infinity, {(15*c^4)/k0^2, 0, (105*c^4)/2 - (490*c^6)/k0^2 + ((315*I)*c^5)/k0, 0, -6615*c^6 + (187677*c^8)/(16*k0^2) - ((14175*I)*c^7)/k0 + (2835*I)/2*c^5*k0 + (945*c^4*k0^2)/8, 0, (-165*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1]

besseltransforms/4-2-4

@@ -0,0 +1,2 @@
+-((k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*k0^2))
+SeriesData[k, Infinity, {(48*c^4)/k0^2, (-315*c^5)/k0^2 + ((105*I)*c^4)/k0, 0, (-2835*c^5)/2 + (4725*c^7)/k0^2 - ((4410*I)*c^6)/k0 + (315*I)/2*c^4*k0, 0, (-693*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1]

besseltransforms/4-2-5

@@ -0,0 +1,2 @@
+(-4*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(5*k^5*k0^2)
+SeriesData[k, Infinity, {(105*c^4)/k0^2, (-1152*c^5)/k0^2 + ((384*I)*c^4)/k0, (-945*c^4)/2 + (4410*c^6)/k0^2 - ((2835*I)*c^5)/k0, 0, 24255*c^6 - (688149*c^8)/(16*k0^2) + ((51975*I)*c^7)/k0 - (10395*I)/2*c^5*k0 - (3465*c^4*k0^2)/8, 0, (429*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1]

besseltransforms/4-2-6

@@ -0,0 +1,2 @@
+(-3*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 18*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 48*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 96*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 12*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 32*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 3*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(3*k^6*k0^2)
+SeriesData[k, Infinity, {(192*c^4)/k0^2, (-2835*c^5)/k0^2 + ((945*I)*c^4)/k0, -1920*c^4 + (17920*c^6)/k0^2 - ((11520*I)*c^5)/k0, (31185*c^5)/2 - (51975*c^7)/k0^2 + ((48510*I)*c^6)/k0 - (3465*I)/2*c^4*k0, 0, (3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 4, 11, 1]

besseltransforms/4-2-7

@@ -0,0 +1,2 @@
+(-4*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7) + 6*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7) - 4*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7) + k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(7*k^7*k0^2)
+SeriesData[k, Infinity, {(315*c^4)/k0^2, (-1920*(3*c^5 - I*c^4*k0))/k0^2, (3465*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^2), (-7680*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^2, (9009*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^2), 0, (-2145*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1]

besseltransforms/4-3-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -5 c x + I k0 x        c x 4                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   3             23/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-3-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -5 c x + I k0 x        c x 4                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   3             23/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-3-2

@@ -0,0 +1,2 @@
+(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(6*k^2*k0^3)
+SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-70*c^6)/k0^3 + ((45*I)*c^5)/k0^2 + (15*c^4)/(2*k0), 0, (315*I)/2*c^5 + (20853*c^8)/(16*k0^3) - ((1575*I)*c^7)/k0^2 - (735*c^6)/k0 + (105*c^4*k0)/8, 0, (-15*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-3

@@ -0,0 +1,2 @@
+(k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 6*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 4*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(6*k^3*k0^3)
+SeriesData[k, Infinity, {(8*c^4)/k0^3, (-45*c^5)/k0^3 + ((15*I)*c^4)/k0^2, 0, (35*I)/2*c^4 + (525*c^7)/k0^3 - ((490*I)*c^6)/k0^2 - (315*c^5)/(2*k0), 0, (-63*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (165*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-4

@@ -0,0 +1,2 @@
+(-4*(k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(60*k^4*k0^3)
+SeriesData[k, Infinity, {(15*c^4)/k0^3, (-48*(3*c^5 - I*c^4*k0))/k0^3, (35*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (-63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^3), 0, (33*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-5

@@ -0,0 +1,2 @@
+((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(20*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(30*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(120*k^5))/k0^3
+SeriesData[k, Infinity, {(24*c^4)/k0^3, (-315*c^5)/k0^3 + ((105*I)*c^4)/k0^2, (1792*c^6)/k0^3 - ((1152*I)*c^5)/k0^2 - (192*c^4)/k0, (-315*I)/2*c^4 - (4725*c^7)/k0^3 + ((4410*I)*c^6)/k0^2 + (2835*c^5)/(2*k0), 0, (231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (-429*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-6

@@ -0,0 +1,2 @@
+((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(35*k^6) - (2*(k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(105*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(210*k^6))/k0^3
+SeriesData[k, Infinity, {(35*c^4)/k0^3, (-576*c^5)/k0^3 + ((192*I)*c^4)/k0^2, (4410*c^6)/k0^3 - ((2835*I)*c^5)/k0^2 - (945*c^4)/(2*k0), (-640*I)*c^4 - (19200*c^7)/k0^3 + ((17920*I)*c^6)/k0^2 + (5760*c^5)/k0, (10395*I)/2*c^5 + (688149*c^8)/(16*k0^3) - ((51975*I)*c^7)/k0^2 - (24255*c^6)/k0 + (3465*c^4*k0)/8, 0, (-143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(56*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(84*k^7) + (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {(48*c^4)/k0^3, (-945*c^5)/k0^3 + ((315*I)*c^4)/k0^2, (8960*c^6)/k0^3 - ((5760*I)*c^5)/k0^2 - (960*c^4)/k0, (-3465*I)/2*c^4 - (51975*c^7)/k0^3 + ((48510*I)*c^6)/k0^2 + (31185*c^5)/(2*k0), (23040*I)*c^5 + (190656*c^8)/k0^3 - ((230400*I)*c^7)/k0^2 - (107520*c^6)/k0 + 1920*c^4*k0, (-3003*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^3), 0, (2145*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^3)}, 3, 11, 1]

besseltransforms/4-4-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -5 c x + I k0 x        c x 4                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   4             25/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-4-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -5 c x + I k0 x        c x 4                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   4             25/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-4-2

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -5 c x + I k0 x        c x 4                                 2  2              4  4              6  6               8  8      Pi                                                   2  2              4  4               6  6               8  8
+                             -(E                (-1 + E   )  (15 (-43692253605 + 3528645120 k  x  - 590413824 k  x  + 352321536 k  x  + 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k  x  + 681246720 k  x  - 1761607680 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])))
+                                                                                                                                                              4
+Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
+                                                                                                                                                            19/2   4             25/2
+                                                                                                                                                8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/4-4-3

@@ -0,0 +1,2 @@
+(-4*(k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5) + 6*(k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5) - 4*(k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5) + k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(120*k^3*k0^4)
+SeriesData[k, Infinity, {(3*c^4)/k0^4, (-8*(3*c^5 - I*c^4*k0))/k0^4, (5*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), 0, (-7*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (3*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-5*(c - I*k0)^12)/128 + (5*(2*c - I*k0)^12)/32 - (15*(3*c - I*k0)^12)/64 + (5*(4*c - I*k0)^12)/32 - (5*(5*c - I*k0)^12)/128)/(120*k0^4)}, 2, 11, 1]

besseltransforms/4-4-4

@@ -0,0 +1,2 @@
+((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(40*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(60*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(240*k^4))/k0^4
+SeriesData[k, Infinity, {(4*c^4)/k0^4, (-45*c^5)/k0^4 + ((15*I)*c^4)/k0^3, (224*c^6)/k0^4 - ((144*I)*c^5)/k0^3 - (24*c^4)/k0^2, (-35*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 0, (21*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (-33*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1]

besseltransforms/4-4-5

@@ -0,0 +1,2 @@
+((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(140*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(210*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(840*k^5))/k0^4
+SeriesData[k, Infinity, {(5*c^4)/k0^4, (-72*c^5)/k0^4 + ((24*I)*c^4)/k0^3, (490*c^6)/k0^4 - ((315*I)*c^5)/k0^3 - (105*c^4)/(2*k0^2), (-1920*c^7)/k0^4 + ((1792*I)*c^6)/k0^3 + (576*c^5)/k0^2 - ((64*I)*c^4)/k0, (63*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), 0, (-11*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, (143*(682591*c^12 - (1504800*I)*c^11*k0 - 1480380*c^10*k0^2 + (850500*I)*c^9*k0^3 + 312795*c^8*k0^4 - (75600*I)*c^7*k0^5 - 11760*c^6*k0^6 + (1080*I)*c^5*k0^7 + 45*c^4*k0^8))/(640*k0^4)}, 2, 11, 1]

besseltransforms/4-4-6

@@ -0,0 +1,2 @@
+((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1120*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(1680*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(6720*k^6))/k0^4
+SeriesData[k, Infinity, {(6*c^4)/k0^4, (-105*c^5)/k0^4 + ((35*I)*c^4)/k0^3, (896*c^6)/k0^4 - ((576*I)*c^5)/k0^3 - (96*c^4)/k0^2, (-315*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/(2*k0^4), 160*c^4 + (15888*c^8)/k0^4 - ((19200*I)*c^7)/k0^3 - (8960*c^6)/k0^2 + ((1920*I)*c^5)/k0, (-231*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^4), 0, (143*(25080*c^11 - (49346*I)*c^10*k0 - 42525*c^9*k0^2 + (20853*I)*c^8*k0^3 + 6300*c^7*k0^4 - (1176*I)*c^6*k0^5 - 126*c^5*k0^6 + (6*I)*c^4*k0^7))/(32*k0^4)}, 2, 11, 1]

besseltransforms/4-4-7

@@ -0,0 +1,2 @@
+((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(840*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(1260*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(5040*k^7))/k0^4
+SeriesData[k, Infinity, {(7*c^4)/k0^4, (-48*(3*c^5 - I*c^4*k0))/k0^4, (105*(28*c^6 - (18*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^4), (-320*(30*c^7 - (28*I)*c^6*k0 - 9*c^5*k0^2 + I*c^4*k0^3))/k0^4, (693*(993*c^8 - (1200*I)*c^7*k0 - 560*c^6*k0^2 + (120*I)*c^5*k0^3 + 10*c^4*k0^4))/(16*k0^4), (-64*(2025*c^9 - (2979*I)*c^8*k0 - 1800*c^7*k0^2 + (560*I)*c^6*k0^3 + 90*c^5*k0^4 - (6*I)*c^4*k0^5))/k0^4, (143*(49346*c^10 - (85050*I)*c^9*k0 - 62559*c^8*k0^2 + (25200*I)*c^7*k0^3 + 5880*c^6*k0^4 - (756*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^4), 0, ((-13*(c - I*k0)^12)/3072 + (13*(2*c - I*k0)^12)/768 - (13*(3*c - I*k0)^12)/512 + (13*(4*c - I*k0)^12)/768 - (13*(5*c - I*k0)^12)/3072)/k0^4}, 2, 11, 1]

besseltransforms/5-1-0

@@ -0,0 +1,2 @@
+(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 5/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 10/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - 10/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 5/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - 1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0
+SeriesData[k, Infinity, {((-225*I)*c^5)/k + (1575*c^6)/(2*k*k0), 0, (-3675*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (19845*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1]

besseltransforms/5-1-1

@@ -0,0 +1,2 @@
+(-5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 10*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 5*(k^(-1) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(k*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(45*c^5)/(k*k0), 0, (-525*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (11025*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-1-2

@@ -0,0 +1,2 @@
+(-5*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 10*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (2*(5*c - I*k0))/k^2 + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2])) + 1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + (2*(6*c - I*k0))/k^2 - (2*(6*c - I*k0))/(k^2*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {((315*I)*c^5)/k - (2205*c^6)/(2*k*k0), 0, (4725*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (-24255*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1]

besseltransforms/5-1-3

@@ -0,0 +1,2 @@
+((k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(-105*c^5)/(k*k0), 0, (945*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-17325*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-1-4

@@ -0,0 +1,2 @@
+((k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0
+SeriesData[k, Infinity, {((-945*I)*c^5)/k + (6615*c^6)/(2*k*k0), 0, (-10395*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 6, 11, 1]

besseltransforms/5-1-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(k^5*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^5*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(945*c^5)/(k*k0), 0, (-3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (45045*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-1-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (10*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^6*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^6*Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)))/k0
+SeriesData[k, Infinity, {(3840*c^5)/(k*k0), ((10395*I)*c^5)/k - (72765*c^6)/(2*k*k0), 0, (45045*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k*k0), 0, (-135135*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k*k0)}, 5, 11, 1]

besseltransforms/5-1-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(c - I*k0)^2]) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(3*c - I*k0)^2]) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(k^7*Sqrt[1 + k^2/(5*c - I*k0)^2]) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2]) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(k^7*Sqrt[1 + k^2/(6*c - I*k0)^2]))/k0
+SeriesData[k, Infinity, {(10395*c^5)/(k*k0), ((46080*I)*c^5)/k - (161280*c^6)/(k*k0), (45045*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k*k0), 0, (-225225*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k*k0)}, 5, 11, 1]

besseltransforms/5-2-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                           -6 c x + I k0 x     Pi                       -5 c x + I k0 x     Pi                       -4 c x + I k0 x     Pi                       -3 c x + I k0 x     Pi                       -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                   -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                   -(c x) + I k0 x     Pi                -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                -(c x) + I k0 x     Pi             -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi             -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                        -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                        -(c x) + I k0 x     Pi                    -6 c x + I k0 x     Pi                     -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi           -6 c x + I k0 x     Pi             -5 c x + I k0 x     Pi             -4 c x + I k0 x     Pi             -3 c x + I k0 x     Pi             -2 c x + I k0 x     Pi           -(c x) + I k0 x     Pi
+                             -13043905875 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   13043905875 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   9 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   9 E                Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   418854310875 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   418854310875 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   75 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   75 E                Sin[-- - k x]   E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   E                Sin[-- - k x]
+                                                               4                                            4                                            4                                            4                                            4                                            4                                        4                                         4                                         4                                         4                                         4                                        4                                     4                                      4                                      4                                      4                                      4                                     4                                  4                                   4                                   4                                   4                                   4                                  4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                             4                                              4                                              4                                              4                                              4                                             4                                         4                                          4                                          4                                          4                                          4                                         4                                      4                                       4                                       4                                       4                                       4                                      4                                   4                                    4                                    4                                    4                                    4                                   4                                4                                  4                                  4                                  4                                  4                                4
+Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}.
+                                            17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2                    17/2   2             19/2                 13/2   2             15/2                13/2   2             15/2                 13/2   2             15/2                 13/2   2             15/2                 13/2   2             15/2                 13/2   2             15/2              9/2   2             11/2              9/2   2             11/2               9/2   2             11/2               9/2   2             11/2               9/2   2             11/2               9/2   2             11/2           5/2   2             7/2             5/2   2             7/2             5/2   2             7/2             5/2   2             7/2             5/2   2             7/2            5/2   2             7/2                           2  3/2                                     2  3/2                                       2  3/2                                       2  3/2                                      2  3/2                                     2  3/2                              19/2   2             21/2                     19/2   2             21/2                      19/2   2             21/2                      19/2   2             21/2                      19/2   2             21/2                      19/2   2             21/2                  15/2   2             17/2                 15/2   2             17/2                  15/2   2             17/2                  15/2   2             17/2                  15/2   2             17/2                  15/2   2             17/2              11/2   2             13/2               11/2   2             13/2              11/2   2             13/2               11/2   2             13/2                11/2   2             13/2              11/2   2             13/2            7/2   2             9/2              7/2   2             9/2              7/2   2             9/2              7/2   2             9/2              7/2   2             9/2             7/2   2             9/2           3/2   2             5/2           3/2   2             5/2            3/2   2             5/2            3/2   2             5/2            3/2   2             5/2           3/2   2             5/2
+                                1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x                    Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-2-1

@@ -0,0 +1,2 @@
+((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/(k*k0^2)
+SeriesData[k, Infinity, {(-315*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-11025*c^6)/4 + (99225*c^8)/(8*k0^2) - ((9975*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1]

besseltransforms/5-2-2

@@ -0,0 +1,2 @@
+(-((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) + 5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^2*k0^2)
+SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1995*c^7)/k0^2 - ((2205*I)/2*c^6)/k0, 0, (-1575*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

besseltransforms/5-2-3

@@ -0,0 +1,2 @@
+(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 - 5*k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 - 10*k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 - k^2*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^3*k0^2)
+SeriesData[k, Infinity, {(735*c^6)/(2*k0^2) - ((105*I)*c^5)/k0, 0, (19845*c^6)/4 - (178605*c^8)/(8*k0^2) + ((17955*I)*c^7)/k0 - (945*I)/2*c^5*k0, 0, (3465*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1]

besseltransforms/5-2-4

@@ -0,0 +1,2 @@
+(-(k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) - 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 5*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 10*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 10*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 5*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + k^2*(-2 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(k^4*k0^2)
+SeriesData[k, Infinity, {(105*c^5)/k0^2, 0, (945*c^5)/2 - (5985*c^7)/k0^2 + ((6615*I)/2*c^6)/k0, 0, (3465*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

besseltransforms/5-2-5

@@ -0,0 +1,2 @@
+((k^4*(-5 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(5*k^5) - (k^4*(-5 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/k^5 + (2*(k^4*(-5 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5))/k^5 - (2*(k^4*(-5 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5))/k^5 + (k^4*(-5 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/k^5 - (k^4*(-5 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(5*k^5))/k0^2
+SeriesData[k, Infinity, {(384*c^5)/k0^2, (-6615*c^6)/(2*k0^2) + ((945*I)*c^5)/k0, 0, (-72765*c^6)/4 + (654885*c^8)/(8*k0^2) - ((65835*I)*c^7)/k0 + (3465*I)/2*c^5*k0, 0, (-9009*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1]

besseltransforms/5-2-6

@@ -0,0 +1,2 @@
+((k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(6*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6))/(6*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6))/(3*k^6) - (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6))/(3*k^6) + (5*(k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6))/(6*k^6) - (k^6 - 6*k^4*(-3 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 32*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(6*k^6))/k0^2
+SeriesData[k, Infinity, {(945*c^5)/k0^2, (-13440*c^6)/k0^2 + ((3840*I)*c^5)/k0, (-10395*c^5)/2 + (65835*c^7)/k0^2 - ((72765*I)/2*c^6)/k0, 0, (-15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

besseltransforms/5-2-7

@@ -0,0 +1,2 @@
+((k^6*(-7 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(7*k^7) - (5*(k^6*(-7 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7))/(7*k^7) + (10*(k^6*(-7 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7))/(7*k^7) - (10*(k^6*(-7 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7))/(7*k^7) + (5*(k^6*(-7 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7))/(7*k^7) - (k^6*(-7 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^4*(-7 + 3*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-7 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(7*k^7))/k0^2
+SeriesData[k, Infinity, {(1920*c^5)/k0^2, (-72765*c^6)/(2*k0^2) + ((10395*I)*c^5)/k0, -23040*c^5 + (291840*c^7)/k0^2 - ((161280*I)*c^6)/k0, (945945*c^6)/4 - (8513505*c^8)/(8*k0^2) + ((855855*I)*c^7)/k0 - (45045*I)/2*c^5*k0, 0, (45045*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 5, 11, 1]

besseltransforms/5-3-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                           -6 c x + I k0 x     Pi                       -5 c x + I k0 x     Pi                       -4 c x + I k0 x     Pi                       -3 c x + I k0 x     Pi                       -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                   -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                   -(c x) + I k0 x     Pi                -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                -(c x) + I k0 x     Pi             -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi             -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                        -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                        -(c x) + I k0 x     Pi                    -6 c x + I k0 x     Pi                     -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi           -6 c x + I k0 x     Pi             -5 c x + I k0 x     Pi             -4 c x + I k0 x     Pi             -3 c x + I k0 x     Pi             -2 c x + I k0 x     Pi           -(c x) + I k0 x     Pi
+                             -13043905875 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   13043905875 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   9 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   9 E                Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   418854310875 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   418854310875 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   75 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   75 E                Sin[-- - k x]   E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   E                Sin[-- - k x]
+                                                               4                                            4                                            4                                            4                                            4                                            4                                        4                                         4                                         4                                         4                                         4                                        4                                     4                                      4                                      4                                      4                                      4                                     4                                  4                                   4                                   4                                   4                                   4                                  4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                             4                                              4                                              4                                              4                                              4                                             4                                         4                                          4                                          4                                          4                                          4                                         4                                      4                                       4                                       4                                       4                                       4                                      4                                   4                                    4                                    4                                    4                                    4                                   4                                4                                  4                                  4                                  4                                  4                                4
+Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}.
+                                            17/2   3             21/2                    17/2   3             21/2                    17/2   3             21/2                    17/2   3             21/2                    17/2   3             21/2                    17/2   3             21/2                 13/2   3             17/2                13/2   3             17/2                 13/2   3             17/2                 13/2   3             17/2                 13/2   3             17/2                 13/2   3             17/2              9/2   3             13/2              9/2   3             13/2               9/2   3             13/2               9/2   3             13/2               9/2   3             13/2               9/2   3             13/2           5/2   3             9/2             5/2   3             9/2             5/2   3             9/2             5/2   3             9/2             5/2   3             9/2            5/2   3             9/2                           3  5/2                                     3  5/2                                       3  5/2                                       3  5/2                                      3  5/2                                     3  5/2                              19/2   3             23/2                     19/2   3             23/2                      19/2   3             23/2                      19/2   3             23/2                      19/2   3             23/2                      19/2   3             23/2                  15/2   3             19/2                 15/2   3             19/2                  15/2   3             19/2                  15/2   3             19/2                  15/2   3             19/2                  15/2   3             19/2              11/2   3             15/2               11/2   3             15/2              11/2   3             15/2               11/2   3             15/2                11/2   3             15/2              11/2   3             15/2            7/2   3             11/2            7/2   3             11/2             7/2   3             11/2             7/2   3             11/2             7/2   3             11/2             7/2   3             11/2          3/2   3             7/2           3/2   3             7/2            3/2   3             7/2            3/2   3             7/2            3/2   3             7/2           3/2   3             7/2
+                                1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x                    Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-3-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -6 c x + I k0 x        c x 5                                    2  2              4  4              6  6               8  8      Pi                                         2  2               4  4              6  6               8  8      Pi
+                             -(E                (-1 + E   )  (8 k x (-14783093325 + 1452971520 k  x  - 309657600 k  x  + 251658240 k  x  + 2147483648 k  x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k  x  + 1589575680 k  x  - 587202560 k  x  + 2147483648 k  x ) Sin[-- + k x]))
+                                                                                                                                                                 4                                                                                                            4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                    19/2   3             23/2
+                                                                                                                                        8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-3-2

@@ -0,0 +1,2 @@
+(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 5*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(6*k^2*k0^3)
+SeriesData[k, Infinity, {(105*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1]

besseltransforms/5-3-3

@@ -0,0 +1,2 @@
+((3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4)/(24*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(24*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(12*k^3) - (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(12*k^3) + (5*(3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4))/(24*k^3) - (3*k^4 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4)/(24*k^3))/k0^3
+SeriesData[k, Infinity, {(15*c^5)/k0^3, 0, (-35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (315*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-165*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1]

besseltransforms/5-3-4

@@ -0,0 +1,2 @@
+((k^4*(-15 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(60*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(12*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(6*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(6*k^4) + (k^4*(-15 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(12*k^4) - (k^4*(-15 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-10 + 7*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 24*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(60*k^4))/k0^3
+SeriesData[k, Infinity, {(48*c^5)/k0^3, (-735*c^6)/(2*k0^3) + ((105*I)*c^5)/k0^2, 0, (315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (-693*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1]

besseltransforms/5-3-5

@@ -0,0 +1,2 @@
+((5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(120*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(24*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(12*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(12*k^5) + (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(24*k^5) - (5*k^6 + 12*k^4*(5 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(15 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(120*k^5))/k0^3
+SeriesData[k, Infinity, {(105*c^5)/k0^3, (-1344*c^6)/k0^3 + ((384*I)*c^5)/k0^2, (315*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), 0, (-1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (429*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1]

besseltransforms/5-3-6

@@ -0,0 +1,2 @@
+((k^6*(-35 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(210*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(42*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(21*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(21*k^6) + (k^6*(-35 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(42*k^6) - (k^6*(-35 + 6*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 6*k^4*(-35 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 16*k^2*(-21 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 160*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(210*k^6))/k0^3
+SeriesData[k, Infinity, {(192*c^5)/k0^3, (-6615*c^6)/(2*k0^3) + ((945*I)*c^5)/k0^2, (24320*c^7)/k0^3 - ((13440*I)*c^6)/k0^2 - (1920*c^5)/k0, (-3465*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (3003*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 4, 11, 1]

besseltransforms/5-3-7

@@ -0,0 +1,2 @@
+((7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(336*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8))/(336*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8))/(168*k^7) - (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8))/(168*k^7) + (5*(7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8))/(336*k^7) - (7*k^8 + 24*k^6*(7 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(42 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(14 - 11*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 384*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(336*k^7))/k0^3
+SeriesData[k, Infinity, {(315*c^5)/k0^3, (-6720*c^6)/k0^3 + ((1920*I)*c^5)/k0^2, (3465*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^3), (-7680*I)*c^5 - (362880*c^8)/k0^3 + ((291840*I)*c^7)/k0^2 + (80640*c^6)/k0, (15015*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^3), 0, (-2145*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^3)}, 4, 11, 1]

besseltransforms/5-4-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                              -6 c x + I k0 x        c x 5                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
+                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
+                                                                                                                                                             4
+Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
+                                                                                                                                                          19/2   4             25/2
+                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-4-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                           -6 c x + I k0 x     Pi                       -5 c x + I k0 x     Pi                       -4 c x + I k0 x     Pi                       -3 c x + I k0 x     Pi                       -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                   -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                   -(c x) + I k0 x     Pi                -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                        -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                        -(c x) + I k0 x     Pi                    -6 c x + I k0 x     Pi                     -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi               -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi               -(c x) + I k0 x     Pi             -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi             -(c x) + I k0 x     Pi
+                             -14783093325 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   14783093325 E                Cos[-- + k x]   2837835 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   2837835 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   15 E                Cos[-- + k x]   75 E                Cos[-- + k x]   75 E                Cos[-- + k x]   75 E                Cos[-- + k x]   75 E                Cos[-- + k x]   15 E                Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   5 E                Sqrt[--] Cos[-- + k x]   10 E                Sqrt[--] Cos[-- + k x]   10 E                Sqrt[--] Cos[-- + k x]   5 E                Sqrt[--] Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   468131288625 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   468131288625 E                Sin[-- + k x]   66891825 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   66891825 E                Sin[-- + k x]   72765 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   72765 E                Sin[-- + k x]   105 E                Sin[-- + k x]   525 E                Sin[-- + k x]   525 E                Sin[-- + k x]   525 E                Sin[-- + k x]   525 E                Sin[-- + k x]   105 E                Sin[-- + k x]   3 E                Sin[-- + k x]   15 E                Sin[-- + k x]   15 E                Sin[-- + k x]   15 E                Sin[-- + k x]   15 E                Sin[-- + k x]   3 E                Sin[-- + k x]
+                                                               4                                            4                                            4                                            4                                            4                                            4                                        4                                         4                                         4                                         4                                         4                                        4                                     4                                      4                                      4                                      4                                      4                                     4                                   4                                   4                                   4                                   4                                   4                                   4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                             4                                              4                                              4                                              4                                              4                                             4                                         4                                          4                                          4                                          4                                          4                                         4                                      4                                       4                                       4                                       4                                       4                                      4                                    4                                    4                                    4                                    4                                    4                                    4                                  4                                   4                                   4                                   4                                   4                                  4
+Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------ + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + -------------------------------- does not converge on {0, Infinity}.
+                                            17/2   4             23/2                    17/2   4             23/2                    17/2   4             23/2                    17/2   4             23/2                    17/2   4             23/2                    17/2   4             23/2                 13/2   4             19/2                13/2   4             19/2                 13/2   4             19/2                 13/2   4             19/2                 13/2   4             19/2                 13/2   4             19/2              9/2   4             15/2              9/2   4             15/2               9/2   4             15/2               9/2   4             15/2               9/2   4             15/2               9/2   4             15/2           5/2   4             11/2            5/2   4             11/2            5/2   4             11/2            5/2   4             11/2            5/2   4             11/2            5/2   4             11/2                           4  7/2                                     4  7/2                                       4  7/2                                       4  7/2                                      4  7/2                                     4  7/2                              19/2   4             25/2                     19/2   4             25/2                      19/2   4             25/2                      19/2   4             25/2                      19/2   4             25/2                      19/2   4             25/2                  15/2   4             21/2                 15/2   4             21/2                  15/2   4             21/2                  15/2   4             21/2                  15/2   4             21/2                  15/2   4             21/2              11/2   4             17/2               11/2   4             17/2              11/2   4             17/2               11/2   4             17/2                11/2   4             17/2              11/2   4             17/2            7/2   4             13/2             7/2   4             13/2             7/2   4             13/2             7/2   4             13/2             7/2   4             13/2             7/2   4             13/2            3/2   4             9/2            3/2   4             9/2             3/2   4             9/2             3/2   4             9/2             3/2   4             9/2             3/2   4             9/2
+                                1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x                     Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x             2 k    k0  Sqrt[2 Pi] x             2 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-4-2

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                -6 c x + I k0 x        c x 5                                 2  2              4  4              6  6               8  8      Pi                                                   2  2              4  4               6  6               8  8
+                             -(E                (-1 + E   )  (15 (-43692253605 + 3528645120 k  x  - 590413824 k  x  + 352321536 k  x  + 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (21606059475 - 2421619200 k  x  + 681246720 k  x  - 1761607680 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])))
+                                                                                                                                                              4
+Integrate::idiv: Integral of --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
+                                                                                                                                                            19/2   4             25/2
+                                                                                                                                                8589934592 k     k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-4-3

@@ -0,0 +1,2 @@
+((k^4*(-15 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5)/(120*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5)/(24*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5)/(12*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5)/(12*k^3) + (k^4*(-15 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5)/(24*k^3) - (k^4*(-15 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 4*k^2*(-5 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5)/(120*k^3))/k0^4
+SeriesData[k, Infinity, {(8*c^5)/k0^4, (-105*c^6)/(2*k0^4) + ((15*I)*c^5)/k0^3, 0, (35*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (-63*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (165*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1]

besseltransforms/5-4-4

@@ -0,0 +1,2 @@
+((5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6)/(240*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6)/(48*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6)/(24*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6)/(24*k^4) + (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6)/(48*k^4) - (5*k^6 + 2*k^4*(15 - 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 8*k^2*(5 - 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 - 16*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6)/(240*k^4))/k0^4
+SeriesData[k, Infinity, {(15*c^5)/k0^4, (-168*c^6)/k0^4 + ((48*I)*c^5)/k0^3, (35*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), 0, (-105*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (33*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1]

besseltransforms/5-4-5

@@ -0,0 +1,2 @@
+((k^6*(-35 + 8*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7)/(840*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7)/(168*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7)/(84*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7)/(84*k^5) + (k^6*(-35 + 8*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7)/(168*k^5) - (k^6*(-35 + 8*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 20*k^4*(-7 + 4*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 8*k^2*(-21 + 17*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 64*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7)/(840*k^5))/k0^4
+SeriesData[k, Infinity, {(24*c^5)/k0^4, (-735*c^6)/(2*k0^4) + ((105*I)*c^5)/k0^3, (2432*c^7)/k0^4 - ((1344*I)*c^6)/k0^3 - (192*c^5)/k0^2, (-315*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 0, (231*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (-429*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1]

besseltransforms/5-4-6

@@ -0,0 +1,2 @@
+((35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(6720*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1344*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(672*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(672*k^6) + (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(1344*k^6) - (35*k^8 + 16*k^6*(35 - 12*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 16*k^4*(105 - 64*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^4 + 64*k^2*(28 - 23*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^6 - 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^8)/(6720*k^6))/k0^4
+SeriesData[k, Infinity, {(35*c^5)/k0^4, (-672*c^6)/k0^4 + ((192*I)*c^5)/k0^3, (315*(38*c^7 - (21*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^4), (-30240*c^8)/k0^4 + ((24320*I)*c^7)/k0^3 + (6720*c^6)/k0^2 - ((640*I)*c^5)/k0, (1155*(1087*c^9 - (1134*I)*c^8*k0 - 456*c^7*k0^2 + (84*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^4), 0, (-143*(120332*c^11 - (179487*I)*c^10*k0 - 114135*c^9*k0^2 + (39690*I)*c^8*k0^3 + 7980*c^7*k0^4 - (882*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^4)}, 3, 11, 1]

besseltransforms/5-4-7

@@ -0,0 +1,2 @@
+((k^8*(-105 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^9)/(5040*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^9)/(1008*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^9)/(504*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^9)/(504*k^7) + (k^8*(-105 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^9)/(1008*k^7) - (k^8*(-105 + 16*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 8*k^6*(-105 + 44*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 144*k^4*(-14 + 9*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^5 + 320*k^2*(-6 + 5*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^7 + 640*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^9)/(5040*k^7))/k0^4
+SeriesData[k, Infinity, {(48*c^5)/k0^4, (-2205*c^6)/(2*k0^4) + ((315*I)*c^5)/k0^3, (12160*c^7)/k0^4 - ((6720*I)*c^6)/k0^3 - (960*c^5)/k0^2, (-3465*(189*c^8 - (152*I)*c^7*k0 - 42*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^4), 1920*c^5 + (347840*c^9)/k0^4 - ((362880*I)*c^8)/k0^3 - (145920*c^7)/k0^2 + ((26880*I)*c^6)/k0, (-3003*(8547*c^10 - (10870*I)*c^9*k0 - 5670*c^8*k0^2 + (1520*I)*c^7*k0^3 + 210*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^4), 0, (2145*(141232*c^12 - (240664*I)*c^11*k0 - 179487*c^10*k0^2 + (76090*I)*c^9*k0^3 + 19845*c^8*k0^4 - (3192*I)*c^7*k0^5 - 294*c^6*k0^6 + (12*I)*c^5*k0^7))/(64*k0^4)}, 3, 11, 1]

besseltransforms/5-5-0

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                           -6 c x + I k0 x     Pi                       -5 c x + I k0 x     Pi                       -4 c x + I k0 x     Pi                       -3 c x + I k0 x     Pi                       -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                   -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                   -(c x) + I k0 x     Pi                -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                -(c x) + I k0 x     Pi             -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi             -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                        -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                        -(c x) + I k0 x     Pi                    -6 c x + I k0 x     Pi                     -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi           -6 c x + I k0 x     Pi             -5 c x + I k0 x     Pi             -4 c x + I k0 x     Pi             -3 c x + I k0 x     Pi             -2 c x + I k0 x     Pi           -(c x) + I k0 x     Pi
+                             -13043905875 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   13043905875 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   9 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   45 E                Cos[-- - k x]   9 E                Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   418854310875 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   418854310875 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   75 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   375 E                Sin[-- - k x]   75 E                Sin[-- - k x]   E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   5 E                Sin[-- - k x]   E                Sin[-- - k x]
+                                                               4                                            4                                            4                                            4                                            4                                            4                                        4                                         4                                         4                                         4                                         4                                        4                                     4                                      4                                      4                                      4                                      4                                     4                                  4                                   4                                   4                                   4                                   4                                  4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                             4                                              4                                              4                                              4                                              4                                             4                                         4                                          4                                          4                                          4                                          4                                         4                                      4                                       4                                       4                                       4                                       4                                      4                                   4                                    4                                    4                                    4                                    4                                   4                                4                                  4                                  4                                  4                                  4                                4
+Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - -------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + --------------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}.
+                                            17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                 13/2   5             21/2                13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2              9/2   5             17/2              9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2           5/2   5             13/2           5/2   5             13/2            5/2   5             13/2            5/2   5             13/2            5/2   5             13/2            5/2   5             13/2                          5  9/2                                     5  9/2                                       5  9/2                                       5  9/2                                      5  9/2                                     5  9/2                              19/2   5             27/2                     19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                  15/2   5             23/2                 15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2              11/2   5             19/2               11/2   5             19/2              11/2   5             19/2               11/2   5             19/2                11/2   5             19/2              11/2   5             19/2            7/2   5             15/2            7/2   5             15/2             7/2   5             15/2             7/2   5             15/2             7/2   5             15/2             7/2   5             15/2         3/2   5             11/2          3/2   5             11/2           3/2   5             11/2           3/2   5             11/2           3/2   5             11/2          3/2   5             11/2
+                                1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x                    Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x          4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            2 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x           4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-5-1

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                           -6 c x + I k0 x     Pi                       -5 c x + I k0 x     Pi                       -4 c x + I k0 x     Pi                       -3 c x + I k0 x     Pi                       -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                   -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                   -(c x) + I k0 x     Pi                -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                        -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                        -(c x) + I k0 x     Pi                    -6 c x + I k0 x     Pi                     -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi               -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi               -(c x) + I k0 x     Pi             -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi             -(c x) + I k0 x     Pi
+                             -14783093325 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   73915466625 E                Cos[-- + k x]   14783093325 E                Cos[-- + k x]   2837835 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   14189175 E                Cos[-- + k x]   2837835 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   23625 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   15 E                Cos[-- + k x]   75 E                Cos[-- + k x]   75 E                Cos[-- + k x]   75 E                Cos[-- + k x]   75 E                Cos[-- + k x]   15 E                Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   5 E                Sqrt[--] Cos[-- + k x]   10 E                Sqrt[--] Cos[-- + k x]   10 E                Sqrt[--] Cos[-- + k x]   5 E                Sqrt[--] Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   468131288625 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   2340656443125 E                Sin[-- + k x]   468131288625 E                Sin[-- + k x]   66891825 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   334459125 E                Sin[-- + k x]   66891825 E                Sin[-- + k x]   72765 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   363825 E                Sin[-- + k x]   72765 E                Sin[-- + k x]   105 E                Sin[-- + k x]   525 E                Sin[-- + k x]   525 E                Sin[-- + k x]   525 E                Sin[-- + k x]   525 E                Sin[-- + k x]   105 E                Sin[-- + k x]   3 E                Sin[-- + k x]   15 E                Sin[-- + k x]   15 E                Sin[-- + k x]   15 E                Sin[-- + k x]   15 E                Sin[-- + k x]   3 E                Sin[-- + k x]
+                                                               4                                            4                                            4                                            4                                            4                                            4                                        4                                         4                                         4                                         4                                         4                                        4                                     4                                      4                                      4                                      4                                      4                                     4                                   4                                   4                                   4                                   4                                   4                                   4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                             4                                              4                                              4                                              4                                              4                                             4                                         4                                          4                                          4                                          4                                          4                                         4                                      4                                       4                                       4                                       4                                       4                                      4                                    4                                    4                                    4                                    4                                    4                                    4                                  4                                   4                                   4                                   4                                   4                                  4
+Integrate::idiv: Integral of ------------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------ + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + -------------------------------- does not converge on {0, Infinity}.
+                                            17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                    17/2   5             25/2                 13/2   5             21/2                13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2              9/2   5             17/2              9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2           5/2   5             13/2            5/2   5             13/2            5/2   5             13/2            5/2   5             13/2            5/2   5             13/2            5/2   5             13/2                           5  9/2                                     5  9/2                                       5  9/2                                       5  9/2                                      5  9/2                                     5  9/2                              19/2   5             27/2                     19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                  15/2   5             23/2                 15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2              11/2   5             19/2               11/2   5             19/2              11/2   5             19/2               11/2   5             19/2                11/2   5             19/2              11/2   5             19/2            7/2   5             15/2             7/2   5             15/2             7/2   5             15/2             7/2   5             15/2             7/2   5             15/2             7/2   5             15/2           3/2   5             11/2            3/2   5             11/2            3/2   5             11/2            3/2   5             11/2            3/2   5             11/2           3/2   5             11/2
+                                1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x           64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            32 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x            64 k    k0  Sqrt[2 Pi] x                     Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x           16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x          131072 k     k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            256 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x             2 k    k0  Sqrt[2 Pi] x             2 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x            4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-5-2

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                          -6 c x + I k0 x     Pi                        -5 c x + I k0 x     Pi                        -4 c x + I k0 x     Pi                        -3 c x + I k0 x     Pi                        -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                   -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                   -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi               -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi               -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                        -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                        -(c x) + I k0 x     Pi                     -6 c x + I k0 x     Pi                     -5 c x + I k0 x     Pi                     -4 c x + I k0 x     Pi                     -3 c x + I k0 x     Pi                     -2 c x + I k0 x     Pi                     -(c x) + I k0 x     Pi                  -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                  -(c x) + I k0 x     Pi               -6 c x + I k0 x     Pi                -5 c x + I k0 x     Pi                -4 c x + I k0 x     Pi                -3 c x + I k0 x     Pi                -2 c x + I k0 x     Pi               -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi              -5 c x + I k0 x     Pi              -4 c x + I k0 x     Pi              -3 c x + I k0 x     Pi              -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi
+                             21606059475 E                Cos[-- - k x]   108030297375 E                Cos[-- - k x]   108030297375 E                Cos[-- - k x]   108030297375 E                Cos[-- - k x]   108030297375 E                Cos[-- - k x]   21606059475 E                Cos[-- - k x]   4729725 E                Cos[-- - k x]   23648625 E                Cos[-- - k x]   23648625 E                Cos[-- - k x]   23648625 E                Cos[-- - k x]   23648625 E                Cos[-- - k x]   4729725 E                Cos[-- - k x]   10395 E                Cos[-- - k x]   51975 E                Cos[-- - k x]   51975 E                Cos[-- - k x]   51975 E                Cos[-- - k x]   51975 E                Cos[-- - k x]   10395 E                Cos[-- - k x]   105 E                Cos[-- - k x]   525 E                Cos[-- - k x]   525 E                Cos[-- - k x]   525 E                Cos[-- - k x]   525 E                Cos[-- - k x]   105 E                Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   10 E                Sqrt[--] Cos[-- - k x]   5 E                Sqrt[--] Cos[-- - k x]   E                Sqrt[--] Cos[-- - k x]   655383804075 E                Sin[-- - k x]   3276919020375 E                Sin[-- - k x]   3276919020375 E                Sin[-- - k x]   3276919020375 E                Sin[-- - k x]   3276919020375 E                Sin[-- - k x]   655383804075 E                Sin[-- - k x]   103378275 E                Sin[-- - k x]   516891375 E                Sin[-- - k x]   516891375 E                Sin[-- - k x]   516891375 E                Sin[-- - k x]   516891375 E                Sin[-- - k x]   103378275 E                Sin[-- - k x]   135135 E                Sin[-- - k x]   675675 E                Sin[-- - k x]   675675 E                Sin[-- - k x]   675675 E                Sin[-- - k x]   675675 E                Sin[-- - k x]   135135 E                Sin[-- - k x]   315 E                Sin[-- - k x]   1575 E                Sin[-- - k x]   1575 E                Sin[-- - k x]   1575 E                Sin[-- - k x]   1575 E                Sin[-- - k x]   315 E                Sin[-- - k x]   15 E                Sin[-- - k x]   75 E                Sin[-- - k x]   75 E                Sin[-- - k x]   75 E                Sin[-- - k x]   75 E                Sin[-- - k x]   15 E                Sin[-- - k x]
+                                                              4                                             4                                             4                                             4                                             4                                            4                                        4                                         4                                         4                                         4                                         4                                        4                                      4                                      4                                      4                                      4                                      4                                      4                                    4                                    4                                    4                                    4                                    4                                    4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                             4                                              4                                              4                                              4                                              4                                             4                                          4                                          4                                          4                                          4                                          4                                          4                                       4                                       4                                       4                                       4                                       4                                       4                                    4                                     4                                     4                                     4                                     4                                    4                                   4                                   4                                   4                                   4                                   4                                   4
+Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- - --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + ------------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}.
+                                           17/2   5             25/2                     17/2   5             25/2                    17/2   5             25/2                     17/2   5             25/2                      17/2   5             25/2                    17/2   5             25/2                 13/2   5             21/2                13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2              9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2               9/2   5             17/2             5/2   5             13/2             5/2   5             13/2             5/2   5             13/2             5/2   5             13/2             5/2   5             13/2             5/2   5             13/2                           5  9/2                                     5  9/2                                       5  9/2                                       5  9/2                                      5  9/2                                     5  9/2                              19/2   5             27/2                     19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                  15/2   5             23/2                11/2   5             19/2               11/2   5             19/2              11/2   5             19/2               11/2   5             19/2                11/2   5             19/2               11/2   5             19/2            7/2   5             15/2              7/2   5             15/2              7/2   5             15/2              7/2   5             15/2              7/2   5             15/2             7/2   5             15/2            3/2   5             11/2            3/2   5             11/2            3/2   5             11/2            3/2   5             11/2            3/2   5             11/2            3/2   5             11/2
+                               1073741824 k     k0  Sqrt[2 Pi] x             1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x              536870912 k     k0  Sqrt[2 Pi] x              1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x           16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x             64 k    k0  Sqrt[2 Pi] x             64 k    k0  Sqrt[2 Pi] x             32 k    k0  Sqrt[2 Pi] x             32 k    k0  Sqrt[2 Pi] x             64 k    k0  Sqrt[2 Pi] x             64 k    k0  Sqrt[2 Pi] x                     Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x             8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           65536 k     k0  Sqrt[2 Pi] x            65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x           512 k    k0  Sqrt[2 Pi] x             512 k    k0  Sqrt[2 Pi] x             256 k    k0  Sqrt[2 Pi] x             256 k    k0  Sqrt[2 Pi] x             512 k    k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x             2 k    k0  Sqrt[2 Pi] x             2 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

besseltransforms/5-5-3

@@ -0,0 +1,9 @@
+Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
+
+                                          -6 c x + I k0 x     Pi                        -5 c x + I k0 x     Pi                        -4 c x + I k0 x     Pi                        -3 c x + I k0 x     Pi                        -2 c x + I k0 x     Pi                       -(c x) + I k0 x     Pi                    -6 c x + I k0 x     Pi                    -5 c x + I k0 x     Pi                    -4 c x + I k0 x     Pi                    -3 c x + I k0 x     Pi                    -2 c x + I k0 x     Pi                    -(c x) + I k0 x     Pi                 -6 c x + I k0 x     Pi                  -5 c x + I k0 x     Pi                  -4 c x + I k0 x     Pi                  -3 c x + I k0 x     Pi                  -2 c x + I k0 x     Pi                 -(c x) + I k0 x     Pi               -6 c x + I k0 x     Pi                -5 c x + I k0 x     Pi                -4 c x + I k0 x     Pi                -3 c x + I k0 x     Pi                -2 c x + I k0 x     Pi               -(c x) + I k0 x     Pi           -6 c x + I k0 x      2       Pi             -5 c x + I k0 x      2       Pi              -4 c x + I k0 x      2       Pi              -3 c x + I k0 x      2       Pi             -2 c x + I k0 x      2       Pi           -(c x) + I k0 x      2       Pi                         -6 c x + I k0 x     Pi                         -5 c x + I k0 x     Pi                         -4 c x + I k0 x     Pi                         -3 c x + I k0 x     Pi                         -2 c x + I k0 x     Pi                         -(c x) + I k0 x     Pi                     -6 c x + I k0 x     Pi                      -5 c x + I k0 x     Pi                      -4 c x + I k0 x     Pi                      -3 c x + I k0 x     Pi                      -2 c x + I k0 x     Pi                     -(c x) + I k0 x     Pi                  -6 c x + I k0 x     Pi                   -5 c x + I k0 x     Pi                   -4 c x + I k0 x     Pi                   -3 c x + I k0 x     Pi                   -2 c x + I k0 x     Pi                  -(c x) + I k0 x     Pi                -6 c x + I k0 x     Pi                 -5 c x + I k0 x     Pi                 -4 c x + I k0 x     Pi                 -3 c x + I k0 x     Pi                 -2 c x + I k0 x     Pi                -(c x) + I k0 x     Pi              -6 c x + I k0 x     Pi               -5 c x + I k0 x     Pi               -4 c x + I k0 x     Pi               -3 c x + I k0 x     Pi               -2 c x + I k0 x     Pi              -(c x) + I k0 x     Pi
+                             41247931725 E                Cos[-- + k x]   206239658625 E                Cos[-- + k x]   206239658625 E                Cos[-- + k x]   206239658625 E                Cos[-- + k x]   206239658625 E                Cos[-- + k x]   41247931725 E                Cos[-- + k x]   11486475 E                Cos[-- + k x]   57432375 E                Cos[-- + k x]   57432375 E                Cos[-- + k x]   57432375 E                Cos[-- + k x]   57432375 E                Cos[-- + k x]   11486475 E                Cos[-- + k x]   45045 E                Cos[-- + k x]   225225 E                Cos[-- + k x]   225225 E                Cos[-- + k x]   225225 E                Cos[-- + k x]   225225 E                Cos[-- + k x]   45045 E                Cos[-- + k x]   945 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   945 E                Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   5 E                Sqrt[--] Cos[-- + k x]   10 E                Sqrt[--] Cos[-- + k x]   10 E                Sqrt[--] Cos[-- + k x]   5 E                Sqrt[--] Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   1159525191825 E                Sin[-- + k x]   5797625959125 E                Sin[-- + k x]   5797625959125 E                Sin[-- + k x]   5797625959125 E                Sin[-- + k x]   5797625959125 E                Sin[-- + k x]   1159525191825 E                Sin[-- + k x]   218243025 E                Sin[-- + k x]   1091215125 E                Sin[-- + k x]   1091215125 E                Sin[-- + k x]   1091215125 E                Sin[-- + k x]   1091215125 E                Sin[-- + k x]   218243025 E                Sin[-- + k x]   405405 E                Sin[-- + k x]   2027025 E                Sin[-- + k x]   2027025 E                Sin[-- + k x]   2027025 E                Sin[-- + k x]   2027025 E                Sin[-- + k x]   405405 E                Sin[-- + k x]   3465 E                Sin[-- + k x]   17325 E                Sin[-- + k x]   17325 E                Sin[-- + k x]   17325 E                Sin[-- + k x]   17325 E                Sin[-- + k x]   3465 E                Sin[-- + k x]   35 E                Sin[-- + k x]   175 E                Sin[-- + k x]   175 E                Sin[-- + k x]   175 E                Sin[-- + k x]   175 E                Sin[-- + k x]   35 E                Sin[-- + k x]
+                                                              4                                             4                                             4                                             4                                             4                                            4                                         4                                         4                                         4                                         4                                         4                                         4                                      4                                       4                                       4                                       4                                       4                                      4                                    4                                     4                                     4                                     4                                     4                                    4                                 Pi      4                                   Pi      4                                    Pi      4                                    Pi      4                                   Pi      4                                 Pi      4                                              4                                              4                                              4                                              4                                              4                                              4                                          4                                           4                                           4                                           4                                           4                                          4                                       4                                        4                                        4                                        4                                        4                                       4                                     4                                      4                                      4                                      4                                      4                                     4                                   4                                    4                                    4                                    4                                    4                                   4
+Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ---------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}.
+                                           17/2   5             25/2                     17/2   5             25/2                    17/2   5             25/2                     17/2   5             25/2                      17/2   5             25/2                    17/2   5             25/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2                 13/2   5             21/2               9/2   5             17/2                9/2   5             17/2               9/2   5             17/2                9/2   5             17/2                 9/2   5             17/2               9/2   5             17/2             5/2   5             13/2             5/2   5             13/2              5/2   5             13/2              5/2   5             13/2              5/2   5             13/2              5/2   5             13/2                           5  9/2                                     5  9/2                                       5  9/2                                       5  9/2                                      5  9/2                                     5  9/2                              19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                      19/2   5             27/2                   15/2   5             23/2                   15/2   5             23/2                  15/2   5             23/2                   15/2   5             23/2                    15/2   5             23/2                  15/2   5             23/2                11/2   5             19/2               11/2   5             19/2                11/2   5             19/2                11/2   5             19/2                11/2   5             19/2                11/2   5             19/2             7/2   5             15/2              7/2   5             15/2               7/2   5             15/2               7/2   5             15/2               7/2   5             15/2               7/2   5             15/2            3/2   5             11/2            3/2   5             11/2             3/2   5             11/2             3/2   5             11/2             3/2   5             11/2             3/2   5             11/2
+                               1073741824 k     k0  Sqrt[2 Pi] x             1073741824 k     k0  Sqrt[2 Pi] x             536870912 k     k0  Sqrt[2 Pi] x              536870912 k     k0  Sqrt[2 Pi] x              1073741824 k     k0  Sqrt[2 Pi] x            1073741824 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            1048576 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            2097152 k     k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x             16384 k    k0  Sqrt[2 Pi] x             8192 k    k0  Sqrt[2 Pi] x              8192 k    k0  Sqrt[2 Pi] x              16384 k    k0  Sqrt[2 Pi] x            16384 k    k0  Sqrt[2 Pi] x             64 k    k0  Sqrt[2 Pi] x             64 k    k0  Sqrt[2 Pi] x              32 k    k0  Sqrt[2 Pi] x              32 k    k0  Sqrt[2 Pi] x              64 k    k0  Sqrt[2 Pi] x              64 k    k0  Sqrt[2 Pi] x                     Sqrt[k] k0  x                              Sqrt[k] k0  x                                Sqrt[k] k0  x                                Sqrt[k] k0  x                               Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              4294967296 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x             16777216 k     k0  Sqrt[2 Pi] x             16777216 k     k0  Sqrt[2 Pi] x             8388608 k     k0  Sqrt[2 Pi] x              8388608 k     k0  Sqrt[2 Pi] x              16777216 k     k0  Sqrt[2 Pi] x            16777216 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x           131072 k     k0  Sqrt[2 Pi] x             65536 k     k0  Sqrt[2 Pi] x             65536 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x            131072 k     k0  Sqrt[2 Pi] x            512 k    k0  Sqrt[2 Pi] x             512 k    k0  Sqrt[2 Pi] x              256 k    k0  Sqrt[2 Pi] x              256 k    k0  Sqrt[2 Pi] x              512 k    k0  Sqrt[2 Pi] x              512 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x             4 k    k0  Sqrt[2 Pi] x              2 k    k0  Sqrt[2 Pi] x              2 k    k0  Sqrt[2 Pi] x              4 k    k0  Sqrt[2 Pi] x              4 k    k0  Sqrt[2 Pi] x
+Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]