qpms/besseltransforms/6-4-2

Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && 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
                             -21606059475 E                Cos[-- - k x]   64818178425 E                Cos[-- - k x]   324090892125 E                Cos[-- - k x]   108030297375 E                Cos[-- - k x]   324090892125 E                Cos[-- - k x]   64818178425 E                Cos[-- - k x]   21606059475 E                Cos[-- - k x]   4729725 E                Cos[-- - k x]   14189175 E                Cos[-- - k x]   70945875 E                Cos[-- - k x]   23648625 E                Cos[-- - k x]   70945875 E                Cos[-- - k x]   14189175 E                Cos[-- - k x]   4729725 E                Cos[-- - k x]   10395 E                Cos[-- - k x]   31185 E                Cos[-- - k x]   155925 E                Cos[-- - k x]   51975 E                Cos[-- - k x]   155925 E                Cos[-- - k x]   31185 E                Cos[-- - k x]   10395 E                Cos[-- - k x]   105 E                Cos[-- - k x]   315 E                Cos[-- - k x]   1575 E                Cos[-- - k x]   525 E                Cos[-- - k x]   1575 E                Cos[-- - k x]   315 E                Cos[-- - k x]   105 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]   655383804075 E                Sin[-- - k x]   1966151412225 E                Sin[-- - k x]   9830757061125 E                Sin[-- - k x]   3276919020375 E                Sin[-- - k x]   9830757061125 E                Sin[-- - k x]   1966151412225 E                Sin[-- - k x]   655383804075 E                Sin[-- - k x]   103378275 E                Sin[-- - k x]   310134825 E                Sin[-- - k x]   1550674125 E                Sin[-- - k x]   516891375 E                Sin[-- - k x]   1550674125 E                Sin[-- - k x]   310134825 E                Sin[-- - k x]   103378275 E                Sin[-- - k x]   135135 E                Sin[-- - k x]   405405 E                Sin[-- - k x]   2027025 E                Sin[-- - k x]   675675 E                Sin[-- - k x]   2027025 E                Sin[-- - k x]   405405 E                Sin[-- - k x]   135135 E                Sin[-- - k x]   315 E                Sin[-- - k x]   945 E                Sin[-- - k x]   4725 E                Sin[-- - k x]   1575 E                Sin[-- - k x]   4725 E                Sin[-- - k x]   945 E                Sin[-- - k x]   315 E                Sin[-- - k x]   15 E                Sin[-- - k x]   45 E                Sin[-- - k x]   225 E                Sin[-- - k x]   75 E                Sin[-- - k x]   225 E                Sin[-- - k x]   45 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                                    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   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                    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                 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               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             5/2   4             11/2                           4  7/2                                     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                      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                  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                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             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             3/2   4             9/2
                                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[2, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 2 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]