qpms/besseltransforms/klarge/5-5-3

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))

                                                                                                                                                                                                            2  2              4  4               6  6               8  8
                              -5 c x + I k0 x        c x 5                                    2  2               4  4                6  6               8  8      Pi          35 (33129291195 - 3192583680 k  x  + 759103488 k  x  - 1660944384 k  x  + 2147483648 k  x ) (Cos[k x] + Sin[k x])
                             E                (-1 + E   )  (8 k x (-41247931725 + 5881075200 k  x  - 2952069120 k  x  - 15854469120 k  x  + 2147483648 k  x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------)
                                                                                                                                                                  4                                                                Sqrt[2]
Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.
                                                                                                                                                        19/2   5             27/2
                                                                                                                                            8589934592 k     k0  Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5 && k > k0 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]

Simplify::time: Time spent on a transformation exceeded 300. seconds, and the transformation was aborted. Increasing the value of TimeConstraint option may improve the result of simplification.
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]
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[3, kx])/(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,Ik0x)Power(1 - Power(E,-(cx)),5)BesselJ(3,kx))/(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))`

Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 2018-03-28 11:52:50 +03:00			`2 2 4 4 6 6 8 8`
			`-5 c x + I k0 x c x 5 2 2 4 4 6 6 8 8 Pi 35 (33129291195 - 3192583680 k x + 759103488 k x - 1660944384 k x + 2147483648 k x ) (Cos[k x] + Sin[k x])`
			`E (-1 + E ) (8 k x (-41247931725 + 5881075200 k x - 2952069120 k x - 15854469120 k x + 2147483648 k x ) Cos[-- + k x] - -----------------------------------------------------------------------------------------------------------------)`
			`4 Sqrt[2]`
			`Integrate::idiv: Integral of ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- does not converge on {0, Infinity}.`
			`19/2 5 27/2`
			`8589934592 k k0 Sqrt[2 Pi] x`
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[3, kx])/(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.`
			`Integrate[(E^(Ik0x)(1 - E^(-(cx)))^5BesselJ[3, kx])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 5]`