qpms/besseltransforms/5-5-2

Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[2, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 2 && q == 5 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]

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