qpms/besseltransforms/klarge/5-4-0

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))

                              -5 c x + I k0 x        c x 5                                2  2               4  4               6  6               8  8      Pi                                                   2  2              4  4              6  6               8  8
                             E                (-1 + E   )  ((-418854310875 + 29682132480 k  x  - 3901685760 k  x  + 1258291200 k  x  - 2147483648 k  x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k  x  + 240844800 k  x  - 150994944 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x]))
                                                                                                                                                             4
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.
                                                                                                                                                          19/2   4             25/2
                                                                                                                                              8589934592 k     k0  Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]
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]
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			`Integrate[(E^(Ik0x)(1 - E^(-(cx)))^5BesselJ[0, kx])/(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,Ik0x)Power(1 - Power(E,-(cx)),5)BesselJ(0,kx))/(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))`

Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 2018-03-28 11:52:50 +03:00			`-5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 2 2 4 4 6 6 8 8`
			`E (-1 + E ) ((-418854310875 + 29682132480 k x - 3901685760 k x + 1258291200 k x - 2147483648 k x ) Cos[-- + k x] + 4 Sqrt[2] k x (13043905875 - 1229437440 k x + 240844800 k x - 150994944 k x + 2147483648 k x ) (Cos[k x] + Sin[k x]))`
			`4`
			`Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ does not converge on {0, Infinity}.`
			`19/2 4 25/2`
			`8589934592 k k0 Sqrt[2 Pi] x`
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			`Series[Integrate[(E^(Ik0x)(1 - E^(-(cx)))^5BesselJ[0, kx])/(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}]`
			`Integrate[(E^(Ik0x)(1 - E^(-(cx)))^5BesselJ[0, kx])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 5]`