qpms/besseltransforms/6-5-3

Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && 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
                             -41247931725 E                Cos[-- + k x]   123743795175 E                Cos[-- + k x]   618718975875 E                Cos[-- + k x]   206239658625 E                Cos[-- + k x]   618718975875 E                Cos[-- + k x]   123743795175 E                Cos[-- + k x]   41247931725 E                Cos[-- + k x]   11486475 E                Cos[-- + k x]   34459425 E                Cos[-- + k x]   172297125 E                Cos[-- + k x]   57432375 E                Cos[-- + k x]   172297125 E                Cos[-- + k x]   34459425 E                Cos[-- + k x]   11486475 E                Cos[-- + k x]   45045 E                Cos[-- + k x]   135135 E                Cos[-- + k x]   675675 E                Cos[-- + k x]   225225 E                Cos[-- + k x]   675675 E                Cos[-- + k x]   135135 E                Cos[-- + k x]   45045 E                Cos[-- + k x]   945 E                Cos[-- + k x]   2835 E                Cos[-- + k x]   14175 E                Cos[-- + k x]   4725 E                Cos[-- + k x]   14175 E                Cos[-- + k x]   2835 E                Cos[-- + k x]   945 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]   1159525191825 E                Sin[-- + k x]   3478575575475 E                Sin[-- + k x]   17392877877375 E                Sin[-- + k x]   5797625959125 E                Sin[-- + k x]   17392877877375 E                Sin[-- + k x]   3478575575475 E                Sin[-- + k x]   1159525191825 E                Sin[-- + k x]   218243025 E                Sin[-- + k x]   654729075 E                Sin[-- + k x]   3273645375 E                Sin[-- + k x]   1091215125 E                Sin[-- + k x]   3273645375 E                Sin[-- + k x]   654729075 E                Sin[-- + k x]   218243025 E                Sin[-- + k x]   405405 E                Sin[-- + k x]   1216215 E                Sin[-- + k x]   6081075 E                Sin[-- + k x]   2027025 E                Sin[-- + k x]   6081075 E                Sin[-- + k x]   1216215 E                Sin[-- + k x]   405405 E                Sin[-- + k x]   3465 E                Sin[-- + k x]   10395 E                Sin[-- + k x]   51975 E                Sin[-- + k x]   17325 E                Sin[-- + k x]   51975 E                Sin[-- + k x]   10395 E                Sin[-- + k x]   3465 E                Sin[-- + k x]   35 E                Sin[-- + k x]   105 E                Sin[-- + k x]   525 E                Sin[-- + k x]   175 E                Sin[-- + k x]   525 E                Sin[-- + k x]   105 E                Sin[-- + k x]   35 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   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                     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                 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                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              5/2   5             13/2                           5  9/2                                     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                      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                  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                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               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             3/2   5             11/2
                                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[3, k*x])/(k0^5*x^4), {x, 0, Infinity}, Assumptions -> n == 3 && q == 5 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]