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Mathematica bessel transforms 

Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00
This commit is contained in:
Marek Nečada 2018-03-28 11:52:50 +03:00
parent d0890b9d91
commit b6edd04755
73 changed files with 129 additions and 238 deletions
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besseltransforms/2-1-0
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besseltransforms/2-1-1
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besseltransforms/2-1-2
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besseltransforms/2-2-0
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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}]

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besseltransforms/2-2-1
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((-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) ((-2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2
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] Piecewise[{{SeriesData[k, Infinity, {c^2/k0^2, 0, (3*c^2)/2 - (7*c^4)/(4*k0^2) + ((3*I)*c^3)/k0, 0, (31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4)/(8*k0^2), 0, (-5*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k0^2), 0, (7*(511*c^10 - (2550*I)*c^9*k0 - 5715*c^8*k0^2 + (7560*I)*c^7*k0^3 + 6510*c^6*k0^4 - (3780*I)*c^5*k0^5 - 1470*c^4*k0^6 + (360*I)*c^3*k0^7 + 45*c^2*k0^8))/(128*k0^2)}, 2, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, (2*c^2 + k0^2)/(2*k0^2), 0, ((c*(c - I*k0)^3)/4 - (c*(2*c - I*k0)^3)/4 - I/4*(c - I*k0)^3*k0 + I/8*(2*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/8 + (c*(2*c - I*k0)^5)/8 + I/8*(c - I*k0)^5*k0 - I/16*(2*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/64 - (5*c*(2*c - I*k0)^7)/64 - (5*I)/64*(c - I*k0)^7*k0 + (5*I)/128*(2*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/128 + (7*c*(2*c - I*k0)^9)/128 + (7*I)/128*(c - I*k0)^9*k0 - (7*I)/256*(2*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

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besseltransforms/2-2-2
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-(((-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)) (-1 + (4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (2*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2)
SeriesData[k, Infinity, {(2*c^2)/k0^2, (-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] SeriesData[k, Infinity, {(2*c^2)/k0^2, (-3*(c^3 - I*c^2*k0))/k0^2, 0, (5*(3*c^5 - (7*I)*c^4*k0 - 6*c^3*k0^2 + (2*I)*c^2*k0^3))/(4*k0^2), 0, (-7*(9*c^7 - (31*I)*c^6*k0 - 45*c^5*k0^2 + (35*I)*c^4*k0^3 + 15*c^3*k0^4 - (3*I)*c^2*k0^5))/(8*k0^2), 0, (15*(85*c^9 - (381*I)*c^8*k0 - 756*c^7*k0^2 + (868*I)*c^6*k0^3 + 630*c^5*k0^4 - (294*I)*c^4*k0^5 - 84*c^3*k0^6 + (12*I)*c^2*k0^7))/(64*k0^2)}, 2, 11, 1]

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besseltransforms/2-3-0
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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]))
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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}]

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

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besseltransforms/2-3-2
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((-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) (-4*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3)
SeriesData[k, Infinity, {c^2/k0^3, (-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] SeriesData[k, Infinity, {c^2/k0^3, (-2*(c^3 - I*c^2*k0))/k0^3, (7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2)/(4*k0^3), 0, (-31*c^6 + (90*I)*c^5*k0 + 105*c^4*k0^2 - (60*I)*c^3*k0^3 - 15*c^2*k0^4)/(24*k0^3), 0, (127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6)/(64*k0^3), 0, (-511*c^10 + (2550*I)*c^9*k0 + 5715*c^8*k0^2 - (7560*I)*c^7*k0^3 - 6510*c^6*k0^4 + (3780*I)*c^5*k0^5 + 1470*c^4*k0^6 - (360*I)*c^3*k0^7 - 45*c^2*k0^8)/(128*k0^3)}, 1, 11, 1]

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9a2ec0ef6771d8a7db72ddc960cbd1172c4c24e2

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besseltransforms/3-2-0 Normal file
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besseltransforms/3-2-1
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((-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) (-6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
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] Piecewise[{{SeriesData[k, Infinity, {(9*c^4)/(2*k0^2) - ((3*I)*c^3)/k0, 0, (-15*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^2), 0, (105*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^2), 0, (-105*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/8 - (3*c*(2*c - I*k0)^3)/4 + (3*c*(3*c - I*k0)^3)/8 - (3*I)/8*(c - I*k0)^3*k0 + (3*I)/8*(2*c - I*k0)^3*k0 - I/8*(3*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/16 + (3*c*(2*c - I*k0)^5)/8 - (3*c*(3*c - I*k0)^5)/16 + (3*I)/16*(c - I*k0)^5*k0 - (3*I)/16*(2*c - I*k0)^5*k0 + I/16*(3*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/128 - (15*c*(2*c - I*k0)^7)/64 + (15*c*(3*c - I*k0)^7)/128 - (15*I)/128*(c - I*k0)^7*k0 + (15*I)/128*(2*c - I*k0)^7*k0 - (5*I)/128*(3*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/256 + (21*c*(2*c - I*k0)^9)/128 - (21*c*(3*c - I*k0)^9)/256 + (21*I)/256*(c - I*k0)^9*k0 - (21*I)/256*(2*c - I*k0)^9*k0 + (7*I)/256*(3*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

2
besseltransforms/3-2-2 Normal file
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(-1 + (6*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2)/k^2 - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2)/k^2 + (2*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2)/k^2 + Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k0^2)
SeriesData[k, Infinity, {(3*c^3)/k0^2, 0, (-15*(5*c^5 - (6*I)*c^4*k0 - 2*c^3*k0^2))/(4*k0^2), 0, (21*(43*c^7 - (90*I)*c^6*k0 - 75*c^5*k0^2 + (30*I)*c^4*k0^3 + 5*c^3*k0^4))/(8*k0^2), 0, (-15*(3025*c^9 - (8694*I)*c^8*k0 - 10836*c^7*k0^2 + (7560*I)*c^6*k0^3 + 3150*c^5*k0^4 - (756*I)*c^4*k0^5 - 84*c^3*k0^6))/(64*k0^2)}, 3, 11, 1]

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besseltransforms/3-3-0
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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}]

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

4
besseltransforms/3-3-2
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@ -1,2 +1,2 @@
((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 3*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 3*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + (6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2)/(6*k0^3) (6*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + 6*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + (12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + 2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/k^2 + 3*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k0^3)
SeriesData[k, Infinity, {(2*c^3)/k0^3, (-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] SeriesData[k, Infinity, {(2*c^3)/k0^3, (-9*c^4)/(2*k0^3) + ((3*I)*c^3)/k0^2, 0, (5*(9*c^6 - (15*I)*c^5*k0 - 9*c^4*k0^2 + (2*I)*c^3*k0^3))/(4*k0^3), 0, (-21*(69*c^8 - (172*I)*c^7*k0 - 180*c^6*k0^2 + (100*I)*c^5*k0^3 + 30*c^4*k0^4 - (4*I)*c^3*k0^5))/(32*k0^3), 0, (15*(933*c^10 - (3025*I)*c^9*k0 - 4347*c^8*k0^2 + (3612*I)*c^7*k0^3 + 1890*c^6*k0^4 - (630*I)*c^5*k0^5 - 126*c^4*k0^6 + (12*I)*c^3*k0^7))/(64*k0^3)}, 2, 11, 1]

1
besseltransforms/4-1-0.REMOVED.git-id Normal file
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@ -0,0 +1 @@
bee84490a2f9b473adccfa023c6611be883a01a7

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

1
besseltransforms/4-1-1.REMOVED.git-id Normal file
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@ -0,0 +1 @@
a9ad81536da843935e33ae577308937e51c35ca7

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

1
besseltransforms/4-1-2.REMOVED.git-id Normal file
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@ -0,0 +1 @@
8640f89aa7c80f216e563672dd2763f2c7becbce

10
besseltransforms/4-2-0
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@ -1,9 +1 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(-1 + E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 4]
-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}]

2
besseltransforms/4-2-1
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@ -0,0 +1,2 @@
((-4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/k + (6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/k - (4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/k + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/k + (Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/2)/k0^2
Piecewise[{{SeriesData[k, Infinity, {(-3*c^4)/k0^2, 0, (-45*c^4)/2 + (195*c^6)/(2*k0^2) - ((90*I)*c^5)/k0, 0, (6825*c^6)/4 - (25515*c^8)/(16*k0^2) + ((2625*I)*c^7)/k0 - (525*I)*c^5*k0 - (525*c^4*k0^2)/8, 0, (105*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^2)}, 4, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((c*(c - I*k0)^3)/2 - (3*c*(2*c - I*k0)^3)/2 + (3*c*(3*c - I*k0)^3)/2 - (c*(4*c - I*k0)^3)/2 - I/2*(c - I*k0)^3*k0 + (3*I)/4*(2*c - I*k0)^3*k0 - I/2*(3*c - I*k0)^3*k0 + I/8*(4*c - I*k0)^3*k0)/k0^2, 0, (-(c*(c - I*k0)^5)/4 + (3*c*(2*c - I*k0)^5)/4 - (3*c*(3*c - I*k0)^5)/4 + (c*(4*c - I*k0)^5)/4 + I/4*(c - I*k0)^5*k0 - (3*I)/8*(2*c - I*k0)^5*k0 + I/4*(3*c - I*k0)^5*k0 - I/16*(4*c - I*k0)^5*k0)/k0^2, 0, ((5*c*(c - I*k0)^7)/32 - (15*c*(2*c - I*k0)^7)/32 + (15*c*(3*c - I*k0)^7)/32 - (5*c*(4*c - I*k0)^7)/32 - (5*I)/32*(c - I*k0)^7*k0 + (15*I)/64*(2*c - I*k0)^7*k0 - (5*I)/32*(3*c - I*k0)^7*k0 + (5*I)/128*(4*c - I*k0)^7*k0)/k0^2, 0, ((-7*c*(c - I*k0)^9)/64 + (21*c*(2*c - I*k0)^9)/64 - (21*c*(3*c - I*k0)^9)/64 + (7*c*(4*c - I*k0)^9)/64 + (7*I)/64*(c - I*k0)^9*k0 - (21*I)/128*(2*c - I*k0)^9*k0 + (7*I)/64*(3*c - I*k0)^9*k0 - (7*I)/256*(4*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

4
besseltransforms/4-2-2
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@ -1,2 +1,2 @@
-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 6*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^2*k0^2)) (-k^2 + 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 12*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2)
SeriesData[k, Infinity, {(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] SeriesData[k, Infinity, {(30*c^5)/k0^2 - ((15*I)*c^4)/k0, 0, 315*c^5 - (525*c^7)/k0^2 + ((1365*I)/2*c^6)/k0 - (105*I)/2*c^4*k0, 0, (315*(370*c^9 - (729*I)*c^8*k0 - 600*c^7*k0^2 + (260*I)*c^6*k0^3 + 60*c^5*k0^4 - (6*I)*c^4*k0^5))/(16*k0^2)}, 5, 11, 1]

9
besseltransforms/4-3-0
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
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}]

9
besseltransforms/4-3-1
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^4*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 4 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-5 c x + I k0 x c x 4 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
-(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}]

4
besseltransforms/4-3-2
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@ -1,2 +1,2 @@
(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 6*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 12*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 4*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(6*k^2*k0^3) (8*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 12*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 24*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 8*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 16*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 2*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3)
SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-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] SeriesData[k, Infinity, {(3*c^4)/k0^3, 0, (-5*(13*c^6 - (12*I)*c^5*k0 - 3*c^4*k0^2))/(2*k0^3), 0, (105*I)*c^5 + (5103*c^8)/(16*k0^3) - ((525*I)*c^7)/k0^2 - (1365*c^6)/(4*k0) + (105*c^4*k0)/8, 0, (-15*(6821*c^10 - (15540*I)*c^9*k0 - 15309*c^8*k0^2 + (8400*I)*c^7*k0^3 + 2730*c^6*k0^4 - (504*I)*c^5*k0^5 - 42*c^4*k0^6))/(32*k0^3)}, 3, 11, 1]

2
besseltransforms/5-1-0
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(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]

1
besseltransforms/5-1-0.REMOVED.git-id Normal file
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6b5039445ac40a8e4dde06ee71a446ec8c971871

2
besseltransforms/5-1-1
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(-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]

1
besseltransforms/5-1-1.REMOVED.git-id Normal file
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f5594061661eec519d31142141692d67f7b41978

2
besseltransforms/5-1-2
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(-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]

1
besseltransforms/5-1-2.REMOVED.git-id Normal file
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a1c5acb5509b38870c8f208e65cec91b86716900

12
besseltransforms/5-2-0
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Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5]
-6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi
-13043905875 E Cos[-- - k x] 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] 13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x]
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 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}. 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 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 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(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}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 5], {k, Infinity, 10}]

4
besseltransforms/5-2-1
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@ -1,2 +1,2 @@
((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 5*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/(k*k0^2) (-10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
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] Piecewise[{{SeriesData[k, Infinity, {(-225*c^6)/(2*k0^2) + ((45*I)*c^5)/k0, 0, (-7875*c^6)/4 + (39375*c^8)/(8*k0^2) - ((5250*I)*c^7)/k0 + (525*I)/2*c^5*k0, 0, (-2205*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^2)}, 6, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((5*c*(c - I*k0)^3)/8 - (5*c*(2*c - I*k0)^3)/2 + (15*c*(3*c - I*k0)^3)/4 - (5*c*(4*c - I*k0)^3)/2 + (5*c*(5*c - I*k0)^3)/8 - (5*I)/8*(c - I*k0)^3*k0 + (5*I)/4*(2*c - I*k0)^3*k0 - (5*I)/4*(3*c - I*k0)^3*k0 + (5*I)/8*(4*c - I*k0)^3*k0 - I/8*(5*c - I*k0)^3*k0)/k0^2, 0, ((-5*c*(c - I*k0)^5)/16 + (5*c*(2*c - I*k0)^5)/4 - (15*c*(3*c - I*k0)^5)/8 + (5*c*(4*c - I*k0)^5)/4 - (5*c*(5*c - I*k0)^5)/16 + (5*I)/16*(c - I*k0)^5*k0 - (5*I)/8*(2*c - I*k0)^5*k0 + (5*I)/8*(3*c - I*k0)^5*k0 - (5*I)/16*(4*c - I*k0)^5*k0 + I/16*(5*c - I*k0)^5*k0)/k0^2, 0, ((25*c*(c - I*k0)^7)/128 - (25*c*(2*c - I*k0)^7)/32 + (75*c*(3*c - I*k0)^7)/64 - (25*c*(4*c - I*k0)^7)/32 + (25*c*(5*c - I*k0)^7)/128 - (25*I)/128*(c - I*k0)^7*k0 + (25*I)/64*(2*c - I*k0)^7*k0 - (25*I)/64*(3*c - I*k0)^7*k0 + (25*I)/128*(4*c - I*k0)^7*k0 - (5*I)/128*(5*c - I*k0)^7*k0)/k0^2, 0, ((-35*c*(c - I*k0)^9)/256 + (35*c*(2*c - I*k0)^9)/64 - (105*c*(3*c - I*k0)^9)/128 + (35*c*(4*c - I*k0)^9)/64 - (35*c*(5*c - I*k0)^9)/256 + (35*I)/256*(c - I*k0)^9*k0 - (35*I)/128*(2*c - I*k0)^9*k0 + (35*I)/128*(3*c - I*k0)^9*k0 - (35*I)/256*(4*c - I*k0)^9*k0 + (7*I)/256*(5*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

4
besseltransforms/5-2-2
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@ -1,2 +1,2 @@
(-((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) + 5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 5*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2)/(k^2*k0^2) (-k^2 + 10*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 10*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2)
SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (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] SeriesData[k, Infinity, {(-15*c^5)/k0^2, 0, (-315*c^5)/2 + (1050*c^7)/k0^2 - ((1575*I)/2*c^6)/k0, 0, (-1575*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^2)}, 5, 11, 1]

9
besseltransforms/5-3-0
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
-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}]

9
besseltransforms/5-3-1
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-6 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
-(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}]

4
besseltransforms/5-3-2
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@ -1,2 +1,2 @@
(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 5*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 10*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 10*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 5*k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 10*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(6*k^2*k0^3) (10*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 20*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 40*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 20*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 10*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 2*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3)
SeriesData[k, Infinity, {(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] SeriesData[k, Infinity, {(75*c^6)/(2*k0^3) - ((15*I)*c^5)/k0^2, 0, (-105*(75*c^8 - (80*I)*c^7*k0 - 30*c^6*k0^2 + (4*I)*c^5*k0^3))/(8*k0^3), 0, (315*(2025*c^10 - (3310*I)*c^9*k0 - 2250*c^8*k0^2 + (800*I)*c^7*k0^3 + 150*c^6*k0^4 - (12*I)*c^5*k0^5))/(32*k0^3)}, 5, 11, 1]

2
besseltransforms/6-1-0
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@ -1,2 +0,0 @@
(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 6/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 15/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - 20/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 15/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - 6/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + 1/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)))/k0
SeriesData[k, Infinity, {(-225*c^6)/(k*k0), 0, (11025*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (-59535*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1]

1
besseltransforms/6-1-0.REMOVED.git-id Normal file
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@ -0,0 +1 @@
0f102e90aa5931a6786417ff8dc4af328dd43035

2
besseltransforms/6-1-1
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@ -1,2 +0,0 @@
(2/k - 6*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 15*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 20*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 15*(k^(-1) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 6*(k^(-1) - 1/(k*Sqrt[1 + k^2/(6*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(k*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0
SeriesData[k, Infinity, {((-1575*I)*c^6)/k + (6300*c^7)/(k*k0), 0, (-33075*(140*c^9 - (99*I)*c^8*k0 - 24*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k*k0)}, 7, 11, 1]

1
besseltransforms/6-1-1.REMOVED.git-id Normal file
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481803dc1d1b689b8e54b8e3f2965fa3f2ec3ac3

2
besseltransforms/6-1-2
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@ -1,2 +0,0 @@
(-6*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 15*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 20*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 15*(1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (2*(5*c - I*k0))/k^2 + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 6*(1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) - (2*(6*c - I*k0))/k^2 + (2*(6*c - I*k0))/(k^2*Sqrt[1 + k^2/(6*c - I*k0)^2])) + 1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (2*(7*c - I*k0))/k^2 + (2*(7*c - I*k0))/(k^2*Sqrt[1 + k^2/(7*c - I*k0)^2]))/k0
SeriesData[k, Infinity, {(315*c^6)/(k*k0), 0, (-14175*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k*k0), 0, (72765*(3047*c^10 - (2800*I)*c^9*k0 - 990*c^8*k0^2 + (160*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k*k0)}, 6, 11, 1]

1
besseltransforms/6-1-2.REMOVED.git-id Normal file
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9280f56d85a627d34557e5b7ee0692b99af6adf2

9
besseltransforms/6-2-0
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Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x]
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}.
17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 17/2 2 19/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 13/2 2 15/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 9/2 2 11/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 5/2 2 7/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 2 3/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 19/2 2 21/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 15/2 2 17/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 11/2 2 13/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 7/2 2 9/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2 3/2 2 5/2
1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

4
besseltransforms/6-2-1
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@ -1,2 +1,2 @@
((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 15*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 15*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 6*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + (-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0))/(k*k0^2) (-12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 30*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 30*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 12*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
SeriesData[k, Infinity, {(45*c^6)/k0^2, 0, (1575*c^6)/2 - (51975*c^8)/(4*k0^2) + ((6300*I)*c^7)/k0, 0, (-3274425*c^8)/8 + (20155905*c^10)/(16*k0^2) - ((1157625*I)*c^9)/k0 + (66150*I)*c^7*k0 + (33075*c^6*k0^2)/8}, 6, 11, 1] Piecewise[{{SeriesData[k, Infinity, {(45*c^6)/k0^2, 0, (1575*c^6)/2 - (29925*c^8)/(4*k0^2) + ((4725*I)*c^7)/k0, 0, (6615*(1087*c^10 - (1260*I)*c^9*k0 - 570*c^8*k0^2 + (120*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^2)}, 6, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((3*c*(c - I*k0)^3)/4 - (15*c*(2*c - I*k0)^3)/4 + (15*c*(3*c - I*k0)^3)/2 - (15*c*(4*c - I*k0)^3)/2 + (15*c*(5*c - I*k0)^3)/4 - (3*c*(6*c - I*k0)^3)/4 - (3*I)/4*(c - I*k0)^3*k0 + (15*I)/8*(2*c - I*k0)^3*k0 - (5*I)/2*(3*c - I*k0)^3*k0 + (15*I)/8*(4*c - I*k0)^3*k0 - (3*I)/4*(5*c - I*k0)^3*k0 + I/8*(6*c - I*k0)^3*k0)/k0^2, 0, ((-3*c*(c - I*k0)^5)/8 + (15*c*(2*c - I*k0)^5)/8 - (15*c*(3*c - I*k0)^5)/4 + (15*c*(4*c - I*k0)^5)/4 - (15*c*(5*c - I*k0)^5)/8 + (3*c*(6*c - I*k0)^5)/8 + (3*I)/8*(c - I*k0)^5*k0 - (15*I)/16*(2*c - I*k0)^5*k0 + (5*I)/4*(3*c - I*k0)^5*k0 - (15*I)/16*(4*c - I*k0)^5*k0 + (3*I)/8*(5*c - I*k0)^5*k0 - I/16*(6*c - I*k0)^5*k0)/k0^2, 0, ((15*c*(c - I*k0)^7)/64 - (75*c*(2*c - I*k0)^7)/64 + (75*c*(3*c - I*k0)^7)/32 - (75*c*(4*c - I*k0)^7)/32 + (75*c*(5*c - I*k0)^7)/64 - (15*c*(6*c - I*k0)^7)/64 - (15*I)/64*(c - I*k0)^7*k0 + (75*I)/128*(2*c - I*k0)^7*k0 - (25*I)/32*(3*c - I*k0)^7*k0 + (75*I)/128*(4*c - I*k0)^7*k0 - (15*I)/64*(5*c - I*k0)^7*k0 + (5*I)/128*(6*c - I*k0)^7*k0)/k0^2, 0, ((-21*c*(c - I*k0)^9)/128 + (105*c*(2*c - I*k0)^9)/128 - (105*c*(3*c - I*k0)^9)/64 + (105*c*(4*c - I*k0)^9)/64 - (105*c*(5*c - I*k0)^9)/128 + (21*c*(6*c - I*k0)^9)/128 + (21*I)/128*(c - I*k0)^9*k0 - (105*I)/256*(2*c - I*k0)^9*k0 + (35*I)/64*(3*c - I*k0)^9*k0 - (105*I)/256*(4*c - I*k0)^9*k0 + (21*I)/128*(5*c - I*k0)^9*k0 - (7*I)/256*(6*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

4
besseltransforms/6-2-2
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@ -1,2 +1,2 @@
-(((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 15*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 20*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 15*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 6*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2)/(k^2*k0^2)) (-k^2 + 12*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 30*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 40*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 30*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 12*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 2*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2)
SeriesData[k, Infinity, {(-1260*c^7)/k0^2 + ((315*I)*c^6)/k0, 0, -28350*c^7 + (165375*c^9)/k0^2 - ((467775*I)/4*c^8)/k0 + (4725*I)/2*c^6*k0}, 7, 11, 1] SeriesData[k, Infinity, {(-945*c^7)/k0^2 + ((315*I)*c^6)/k0, 0, (4725*(63*c^9 - (57*I)*c^8*k0 - 18*c^7*k0^2 + (2*I)*c^6*k0^3))/(4*k0^2)}, 7, 11, 1]

9
besseltransforms/6-3-0
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x 2 Pi -6 c x + I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -7 c x + I k0 x Pi -6 c x + I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
13043905875 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 195658588125 E Cos[-- - k x] 39131717625 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 2401245 E Cos[-- - k x] 7203735 E Cos[-- - k x] 36018675 E Cos[-- - k x] 12006225 E Cos[-- - k x] 36018675 E Cos[-- - k x] 7203735 E Cos[-- - k x] 2401245 E Cos[-- - k x] 3675 E Cos[-- - k x] 11025 E Cos[-- - k x] 55125 E Cos[-- - k x] 18375 E Cos[-- - k x] 55125 E Cos[-- - k x] 11025 E Cos[-- - k x] 3675 E Cos[-- - k x] 9 E Cos[-- - k x] 27 E Cos[-- - k x] 135 E Cos[-- - k x] 45 E Cos[-- - k x] 135 E Cos[-- - k x] 27 E Cos[-- - k x] 9 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 20 E Sqrt[--] Cos[-- - k x] 15 E Sqrt[--] Cos[-- - k x] 6 E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 6282814663125 E Sin[-- - k x] 1256562932625 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 57972915 E Sin[-- - k x] 173918745 E Sin[-- - k x] 869593725 E Sin[-- - k x] 289864575 E Sin[-- - k x] 869593725 E Sin[-- - k x] 173918745 E Sin[-- - k x] 57972915 E Sin[-- - k x] 59535 E Sin[-- - k x] 178605 E Sin[-- - k x] 893025 E Sin[-- - k x] 297675 E Sin[-- - k x] 893025 E Sin[-- - k x] 178605 E Sin[-- - k x] 59535 E Sin[-- - k x] 75 E Sin[-- - k x] 225 E Sin[-- - k x] 1125 E Sin[-- - k x] 375 E Sin[-- - k x] 1125 E Sin[-- - k x] 225 E Sin[-- - k x] 75 E Sin[-- - k x] E Sin[-- - k x] 3 E Sin[-- - k x] 15 E Sin[-- - k x] 5 E Sin[-- - k x] 15 E Sin[-- - k x] 3 E Sin[-- - k x] E Sin[-- - k x]
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 Pi 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------- - ------------------------------------------ + ------------------------------------------ - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + -------------------------------------- - -------------------------------------- + ----------------------------------- - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - -------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - ---------------------------------- + --------------------------------- - -------------------------------- + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + --------------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + --------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + ----------------------------------- - ---------------------------------- + --------------------------------- - ------------------------------ + -------------------------------- - --------------------------------- + -------------------------------- - --------------------------------- + -------------------------------- - ------------------------------ does not converge on {0, Infinity}.
17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2
1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 268435456 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 524288 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 4096 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 16 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 2147483648 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 4194304 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 32768 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 128 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

9
besseltransforms/6-3-1
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-7 c x + I k0 x c x 6 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
-(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x]))
4 4
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
19/2 3 23/2
8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

4
besseltransforms/6-3-2
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@ -1,2 +1,2 @@
(-6*(((-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/(3*k^2)) + 15*(((-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2)) - 20*(((-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/(3*k^2)) + 15*(((-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/(3*k^2)) - 6*(((-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^2)) + ((-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/(3*k^2) + ((-3 + 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3)/(3*k^2))/k0^3 ((3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3)/k^2 + (5*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0))/2 + (5*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3)/k^2 + (10*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0))/3 - (20*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3)/(3*k^2) + (5*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0))/2 + (5*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3)/k^2 + (3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - (2*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3)/k^2 + ((-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0))/6 + ((-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3)/(3*k^2) + (k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/4)/k0^3
SeriesData[k, Infinity, {(-15*c^6)/k0^3, 0, (315*(33*c^8 - (16*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-9450*I)*c^7 - (2879415*c^10)/(16*k0^3) + ((165375*I)*c^9)/k0^2 + (467775*c^8)/(8*k0) - (4725*c^6*k0)/8}, 5, 11, 1] SeriesData[k, Infinity, {(-15*c^6)/k0^3, 0, (315*(19*c^8 - (12*I)*c^7*k0 - 2*c^6*k0^2))/(4*k0^3), 0, (-945*(1087*c^10 - (1260*I)*c^9*k0 - 570*c^8*k0^2 + (120*I)*c^7*k0^3 + 10*c^6*k0^4))/(16*k0^3)}, 5, 11, 1]

2
besseltransforms/7-1-0
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@ -1,2 +0,0 @@
(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - 7/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + 21/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - 35/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + 35/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - 21/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) + 7/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - 1/(Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)))/k0
SeriesData[k, Infinity, {((11025*I)*c^7)/k - (99225*c^8)/(2*k*k0), 0, (297675*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1]

1
besseltransforms/7-1-0.REMOVED.git-id Normal file
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@ -0,0 +1 @@
ae505b9d4c1eeaa06af2c14fbf57097d2e776630

2
besseltransforms/7-1-1
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@ -1,2 +0,0 @@
(-7*(k^(-1) - 1/(k*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 21*(k^(-1) - 1/(k*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 35*(k^(-1) - 1/(k*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 35*(k^(-1) - 1/(k*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 21*(k^(-1) - 1/(k*Sqrt[1 + k^2/(6*c - I*k0)^2])) + 7*(k^(-1) - 1/(k*Sqrt[1 + k^2/(7*c - I*k0)^2])) - 1/(k*Sqrt[1 + k^2/(c - I*k0)^2]) + 1/(k*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0
SeriesData[k, Infinity, {(-1575*c^7)/(k*k0), 0, (33075*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k*k0)}, 7, 11, 1]

1
besseltransforms/7-1-1.REMOVED.git-id Normal file
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@ -0,0 +1 @@
2ba9a09f1db5bc6a45dd3b7edebf70f39529b350

2
besseltransforms/7-1-2
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@ -1,2 +0,0 @@
(-7*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) + 21*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) - 35*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) + 35*(1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) - (2*(5*c - I*k0))/k^2 + (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2])) - 21*(1/(Sqrt[1 + k^2/(6*c - I*k0)^2]*(6*c - I*k0)) - (2*(6*c - I*k0))/k^2 + (2*(6*c - I*k0))/(k^2*Sqrt[1 + k^2/(6*c - I*k0)^2])) + 7*(1/(Sqrt[1 + k^2/(7*c - I*k0)^2]*(7*c - I*k0)) - (2*(7*c - I*k0))/k^2 + (2*(7*c - I*k0))/(k^2*Sqrt[1 + k^2/(7*c - I*k0)^2])) + 1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2]) - 1/(Sqrt[1 + k^2/(8*c - I*k0)^2]*(8*c - I*k0)) + (2*(8*c - I*k0))/k^2 - (2*(8*c - I*k0))/(k^2*Sqrt[1 + k^2/(8*c - I*k0)^2]))/k0
SeriesData[k, Infinity, {((-14175*I)*c^7)/k + (127575*c^8)/(2*k*k0), 0, (-363825*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k*k0)}, 8, 11, 1]

1
besseltransforms/7-1-2.REMOVED.git-id Normal file
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ffac63299c303e912d85a312d47d1b59b898daf7

9
besseltransforms/7-2-0
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))
4
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
19/2 2 21/2
8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^2*x), {x, 0, Infinity}, Assumptions -> n == 0 && q == 2 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

4
besseltransforms/7-2-1
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@ -1,2 +1,2 @@
((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 7*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 21*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 35*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 35*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 21*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 7*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) - (-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0))/(k*k0^2) (-14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 14*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + k*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (2*Sqrt[k^2 - k0^2])/(k*Sqrt[Pi])] + I*Piecewise[{{(2*k0)/(k*Sqrt[Pi]), k0^2/k^2 < 1}, {(2*(k0 - Sqrt[-k^2 + k0^2]))/(k*Sqrt[Pi]), k0^2/k^2 > 1}}, 0]))/(2*k*k0^2)
SeriesData[k, Infinity, {(14175*c^8)/(2*k0^2) - ((1575*I)*c^7)/k0, 0, (-33075*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1] Piecewise[{{SeriesData[k, Infinity, {(11025*c^8)/(2*k0^2) - ((1575*I)*c^7)/k0, 0, (-33075*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^2)}, 8, 11, 1], (k0 <= 0 && k^2/k0^2 > 1) || k0 > 0}}, SeriesData[k, Infinity, {-k0^(-2), 0, 1/2, 0, ((7*c*(c - I*k0)^3)/8 - (21*c*(2*c - I*k0)^3)/4 + (105*c*(3*c - I*k0)^3)/8 - (35*c*(4*c - I*k0)^3)/2 + (105*c*(5*c - I*k0)^3)/8 - (21*c*(6*c - I*k0)^3)/4 + (7*c*(7*c - I*k0)^3)/8 - (7*I)/8*(c - I*k0)^3*k0 + (21*I)/8*(2*c - I*k0)^3*k0 - (35*I)/8*(3*c - I*k0)^3*k0 + (35*I)/8*(4*c - I*k0)^3*k0 - (21*I)/8*(5*c - I*k0)^3*k0 + (7*I)/8*(6*c - I*k0)^3*k0 - I/8*(7*c - I*k0)^3*k0)/k0^2, 0, ((-7*c*(c - I*k0)^5)/16 + (21*c*(2*c - I*k0)^5)/8 - (105*c*(3*c - I*k0)^5)/16 + (35*c*(4*c - I*k0)^5)/4 - (105*c*(5*c - I*k0)^5)/16 + (21*c*(6*c - I*k0)^5)/8 - (7*c*(7*c - I*k0)^5)/16 + (7*I)/16*(c - I*k0)^5*k0 - (21*I)/16*(2*c - I*k0)^5*k0 + (35*I)/16*(3*c - I*k0)^5*k0 - (35*I)/16*(4*c - I*k0)^5*k0 + (21*I)/16*(5*c - I*k0)^5*k0 - (7*I)/16*(6*c - I*k0)^5*k0 + I/16*(7*c - I*k0)^5*k0)/k0^2, 0, ((35*c*(c - I*k0)^7)/128 - (105*c*(2*c - I*k0)^7)/64 + (525*c*(3*c - I*k0)^7)/128 - (175*c*(4*c - I*k0)^7)/32 + (525*c*(5*c - I*k0)^7)/128 - (105*c*(6*c - I*k0)^7)/64 + (35*c*(7*c - I*k0)^7)/128 - (35*I)/128*(c - I*k0)^7*k0 + (105*I)/128*(2*c - I*k0)^7*k0 - (175*I)/128*(3*c - I*k0)^7*k0 + (175*I)/128*(4*c - I*k0)^7*k0 - (105*I)/128*(5*c - I*k0)^7*k0 + (35*I)/128*(6*c - I*k0)^7*k0 - (5*I)/128*(7*c - I*k0)^7*k0)/k0^2, 0, ((-49*c*(c - I*k0)^9)/256 + (147*c*(2*c - I*k0)^9)/128 - (735*c*(3*c - I*k0)^9)/256 + (245*c*(4*c - I*k0)^9)/64 - (735*c*(5*c - I*k0)^9)/256 + (147*c*(6*c - I*k0)^9)/128 - (49*c*(7*c - I*k0)^9)/256 + (49*I)/256*(c - I*k0)^9*k0 - (147*I)/256*(2*c - I*k0)^9*k0 + (245*I)/256*(3*c - I*k0)^9*k0 - (245*I)/256*(4*c - I*k0)^9*k0 + (147*I)/256*(5*c - I*k0)^9*k0 - (49*I)/256*(6*c - I*k0)^9*k0 + (7*I)/256*(7*c - I*k0)^9*k0)/k0^2}, 0, 11, 1]]

4
besseltransforms/7-2-2
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@ -1,2 +1,2 @@
(-((-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2) + 7*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 21*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 35*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 35*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 21*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 - 7*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + (-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^2)/(k^2*k0^2) (-k^2 + 14*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 42*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 70*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 42*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 14*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^2 + 2*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^2 + k^2*Sqrt[Pi]*(I*Piecewise[{{0, k^2/k0^2 <= 1}}, (2*k0*Sqrt[k^2 - k0^2])/(k^2*Sqrt[Pi])] + Piecewise[{{(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2]))/(k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(1 - (2*k0^2)/k^2)/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(2*k^2*k0^2)
SeriesData[k, Infinity, {(315*c^7)/k0^2, 0, (-4725*(125*c^9 - (54*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1] SeriesData[k, Infinity, {(315*c^7)/k0^2, 0, (-4725*(77*c^9 - (42*I)*c^8*k0 - 6*c^7*k0^2))/(4*k0^2)}, 7, 11, 1]

9
besseltransforms/7-3-0
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))
4
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
19/2 3 23/2
8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

9
besseltransforms/7-3-1
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@ -1,9 +1,2 @@
Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
-8 c x + I k0 x c x 7 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
-(E (-1 + E ) (8 k x (-14783093325 + 1452971520 k x - 309657600 k x + 251658240 k x + 2147483648 k x ) Cos[-- + k x] - 3 (156043762875 - 11416204800 k x + 1589575680 k x - 587202560 k x + 2147483648 k x ) Sin[-- + k x]))
4 4
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
19/2 3 23/2
8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

4
besseltransforms/7-3-2
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@ -1,2 +1,2 @@
(k^2*(-3 + 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) + 2*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 7*k^2*(3 - 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) - 14*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 21*k^2*(-3 + 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) + 42*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 35*k^2*(3 - 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) - 70*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 35*k^2*(-3 + 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) + 70*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 21*k^2*(3 - 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) - 42*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 7*k^2*(-3 + 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) + 14*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + k^2*(3 - 2*Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0) - 2*(-1 + Sqrt[1 + k^2/(8*c - I*k0)^2])*(8*c - I*k0)^3)/(6*k^2*k0^3) (14*k^2*(3 - 2*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0) - 28*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^3 + 42*k^2*(-3 + 2*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0) + 84*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^3 + 70*k^2*(3 - 2*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0) - 140*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^3 + 70*k^2*(-3 + 2*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0) + 140*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^3 + 42*k^2*(3 - 2*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0) - 84*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^3 + 14*k^2*(-3 + 2*Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0) + 28*(-1 + Sqrt[1 + k^2/(6*c - I*k0)^2])*(6*c - I*k0)^3 + 2*k^2*(3 - 2*Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0) - 4*(-1 + Sqrt[1 + k^2/(7*c - I*k0)^2])*(7*c - I*k0)^3 + 3*k^2*k0*Sqrt[Pi]*(Piecewise[{{0, k^2/k0^2 <= 1}}, (4*(k^2 - k0^2)^(3/2))/(3*k^2*k0*Sqrt[Pi])] + I*Piecewise[{{(-2*(2*k0*(k0 - Sqrt[-k^2 + k0^2]) + k^2*(-3 + (2*Sqrt[-k^2 + k0^2])/k0)))/(3*k^2*Sqrt[Pi]), k^2/k0^2 < 1}, {(2*(1 - (2*k0^2)/(3*k^2)))/Sqrt[Pi], k^2/k0^2 > 1}}, 0]))/(12*k^2*k0^3)
SeriesData[k, Infinity, {(-2835*c^8)/(2*k0^3) + ((315*I)*c^7)/k0^2, 0, (4725*(198*c^10 - (125*I)*c^9*k0 - 27*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1] SeriesData[k, Infinity, {(-2205*c^8)/(2*k0^3) + ((315*I)*c^7)/k0^2, 0, (4725*(98*c^10 - (77*I)*c^9*k0 - 21*c^8*k0^2 + (2*I)*c^7*k0^3))/(4*k0^3)}, 7, 11, 1]

14
besseltransforms/klarge/5-3-0
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@ -1,13 +1,11 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8
13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 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 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 4
Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ----------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. 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 19/2 3 23/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 0 && q == 3 && κ == 5]

2
besseltransforms/klarge/5-3-1
View File

@ -8,6 +8,4 @@ Integrate::idiv: Integral of ------------------------------------- - -----------
17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5]

14
besseltransforms/klarge/5-4-0
View File

@ -1,13 +1,11 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8
13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 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 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 4
Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ----------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - -------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. 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 19/2 4 25/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5]

12
besseltransforms/klarge/5-4-1
View File

@ -1,11 +1,11 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,4)*Power(x,3)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi
14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] -(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 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 4 4
Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + -------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. 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 19/2 4 25/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 1 && q == 4 && κ == 5]

14
besseltransforms/klarge/5-5-0
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@ -1,11 +1,13 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(0,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8
13043905875 E Cos[-- - k x] 13043905875 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 65219529375 E Cos[-- - k x] 2401245 E Cos[-- - k x] 2401245 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 12006225 E Cos[-- - k x] 3675 E Cos[-- - k x] 3675 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 18375 E Cos[-- - k x] 9 E Cos[-- - k x] 9 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] 45 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 418854310875 E Sin[-- - k x] 418854310875 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 2094271554375 E Sin[-- - k x] 57972915 E Sin[-- - k x] 57972915 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 289864575 E Sin[-- - k x] 59535 E Sin[-- - k x] 59535 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 297675 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] 375 E Sin[-- - k x] E Sin[-- - k x] E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 5 E Sin[-- - k x] 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 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 4
Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + -------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - --------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- - --------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- + ----------------------------- - --------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - --------------------------- + ------------------------------ - -------------------------------- + -------------------------------- - -------------------------------- + -------------------------------- does not converge on {0, Infinity}. 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 19/2 5 27/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 0 && q == 5 && κ == 5]

12
besseltransforms/klarge/5-5-1
View File

@ -1,12 +1,12 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8 Pi
14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] -(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 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 4 4
Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - ---------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + --------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}. 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 19/2 5 27/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 1 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.

12
besseltransforms/klarge/5-5-2
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@ -1,11 +1,11 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(2,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8
-21606059475 E Cos[-- - k x] 21606059475 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 108030297375 E Cos[-- - k x] 4729725 E Cos[-- - k x] 4729725 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 23648625 E Cos[-- - k x] 10395 E Cos[-- - k x] 10395 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 51975 E Cos[-- - k x] 105 E Cos[-- - k x] 105 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] 525 E Cos[-- - k x] E Sqrt[--] Cos[-- - k x] E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 10 E Sqrt[--] Cos[-- - k x] 5 E Sqrt[--] Cos[-- - k x] 655383804075 E Sin[-- - k x] 655383804075 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 3276919020375 E Sin[-- - k x] 103378275 E Sin[-- - k x] 103378275 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 516891375 E Sin[-- - k x] 135135 E Sin[-- - k x] 135135 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 675675 E Sin[-- - k x] 315 E Sin[-- - k x] 315 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 1575 E Sin[-- - k x] 15 E Sin[-- - k x] 15 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] 75 E Sin[-- - k x] -(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 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 4
Integrate::idiv: Integral of ------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ---------------------------------- - -------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------ + ---------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- - --------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- does not converge on {0, Infinity}. 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 19/2 5 27/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5]

13
besseltransforms/klarge/5-5-3
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@ -1,12 +1,13 @@
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0] Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(3,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0)) Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(3,k*x))/(Power(k0,5)*Power(x,4)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0))
I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x 2 Pi -5 c x + I k0 x 2 Pi -4 c x + I k0 x 2 Pi -3 c x + I k0 x 2 Pi -2 c x + I k0 x 2 Pi -(c x) + I k0 x 2 Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi I k0 x Pi -5 c x + I k0 x Pi -4 c x + I k0 x Pi -3 c x + I k0 x Pi -2 c x + I k0 x Pi -(c x) + I k0 x Pi 2 2 4 4 6 6 8 8
-41247931725 E Cos[-- + k x] 41247931725 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 206239658625 E Cos[-- + k x] 11486475 E Cos[-- + k x] 11486475 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 57432375 E Cos[-- + k x] 45045 E Cos[-- + k x] 45045 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 225225 E Cos[-- + k x] 945 E Cos[-- + k x] 945 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 1159525191825 E Sin[-- + k x] 1159525191825 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 5797625959125 E Sin[-- + k x] 218243025 E Sin[-- + k x] 218243025 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 1091215125 E Sin[-- + k x] 405405 E Sin[-- + k x] 405405 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 2027025 E Sin[-- + k x] 3465 E Sin[-- + k x] 3465 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 17325 E Sin[-- + k x] 35 E Sin[-- + k x] 35 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] 175 E Sin[-- + k x] -5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])
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 E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------)
Integrate::idiv: Integral of ------------------------------------- + ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - ------------------------------------------- + ------------------------------------------- + ---------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- - ------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - ------------------------------------- + ------------------------------------- - ---------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ----------------------------------- + ----------------------------------- + ------------------------------ - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- - ------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- + ----------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- - --------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - -------------------------------------- + -------------------------------------- + ----------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- does not converge on {0, Infinity}. 4 Sqrt[2]
17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 17/2 5 25/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 13/2 5 21/2 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 Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 536870912 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 1048576 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 8192 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 32 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x Sqrt[k] k0 x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 4294967296 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 8388608 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 65536 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 256 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 19/2 5 27/2
8589934592 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}] Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification. Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.