qpms/besseltransforms/7-7-3

Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^7*BesselJ[3, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 3 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0]

                                          -8 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                    -8 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                 -8 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               -8 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           -8 c x + I k0 x      2       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                         -8 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                     -8 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                  -8 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                -8 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              -8 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]   288735522075 E                Cos[-- + k x]   866206566225 E                Cos[-- + k x]   1443677610375 E                Cos[-- + k x]   1443677610375 E                Cos[-- + k x]   866206566225 E                Cos[-- + k x]   288735522075 E                Cos[-- + k x]   41247931725 E                Cos[-- + k x]   11486475 E                Cos[-- + k x]   80405325 E                Cos[-- + k x]   241215975 E                Cos[-- + k x]   402026625 E                Cos[-- + k x]   402026625 E                Cos[-- + k x]   241215975 E                Cos[-- + k x]   80405325 E                Cos[-- + k x]   11486475 E                Cos[-- + k x]   45045 E                Cos[-- + k x]   315315 E                Cos[-- + k x]   945945 E                Cos[-- + k x]   1576575 E                Cos[-- + k x]   1576575 E                Cos[-- + k x]   945945 E                Cos[-- + k x]   315315 E                Cos[-- + k x]   45045 E                Cos[-- + k x]   945 E                Cos[-- + k x]   6615 E                Cos[-- + k x]   19845 E                Cos[-- + k x]   33075 E                Cos[-- + k x]   33075 E                Cos[-- + k x]   19845 E                Cos[-- + k x]   6615 E                Cos[-- + k x]   945 E                Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   7 E                Sqrt[--] Cos[-- + k x]   21 E                Sqrt[--] Cos[-- + k x]   35 E                Sqrt[--] Cos[-- + k x]   35 E                Sqrt[--] Cos[-- + k x]   21 E                Sqrt[--] Cos[-- + k x]   7 E                Sqrt[--] Cos[-- + k x]   E                Sqrt[--] Cos[-- + k x]   1159525191825 E                Sin[-- + k x]   8116676342775 E                Sin[-- + k x]   24350029028325 E                Sin[-- + k x]   40583381713875 E                Sin[-- + k x]   40583381713875 E                Sin[-- + k x]   24350029028325 E                Sin[-- + k x]   8116676342775 E                Sin[-- + k x]   1159525191825 E                Sin[-- + k x]   218243025 E                Sin[-- + k x]   1527701175 E                Sin[-- + k x]   4583103525 E                Sin[-- + k x]   7638505875 E                Sin[-- + k x]   7638505875 E                Sin[-- + k x]   4583103525 E                Sin[-- + k x]   1527701175 E                Sin[-- + k x]   218243025 E                Sin[-- + k x]   405405 E                Sin[-- + k x]   2837835 E                Sin[-- + k x]   8513505 E                Sin[-- + k x]   14189175 E                Sin[-- + k x]   14189175 E                Sin[-- + k x]   8513505 E                Sin[-- + k x]   2837835 E                Sin[-- + k x]   405405 E                Sin[-- + k x]   3465 E                Sin[-- + k x]   24255 E                Sin[-- + k x]   72765 E                Sin[-- + k x]   121275 E                Sin[-- + k x]   121275 E                Sin[-- + k x]   72765 E                Sin[-- + k x]   24255 E                Sin[-- + k x]   3465 E                Sin[-- + k x]   35 E                Sin[-- + k x]   245 E                Sin[-- + k x]   735 E                Sin[-- + k x]   1225 E                Sin[-- + k x]   1225 E                Sin[-- + k x]   735 E                Sin[-- + k x]   245 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                                      4                                      4                                     4                                    4                                 Pi      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                                     4                                     4                                    4                                    4                                   4
Integrate::idiv: Integral of ------------------------------------------ - ------------------------------------------- + ------------------------------------------- - -------------------------------------------- + -------------------------------------------- - ------------------------------------------- + ------------------------------------------- - ------------------------------------------ - --------------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------------ - ------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------ + ---------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ + ----------------------------------- - ---------------------------------- - --------------------------------------- + ----------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ----------------------------------------- + --------------------------------------- + -------------------------------------------- - -------------------------------------------- + --------------------------------------------- - --------------------------------------------- + --------------------------------------------- - --------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ---------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ----------------------------------------- - ----------------------------------------- + ---------------------------------------- + ------------------------------------- - -------------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - -------------------------------------- + -------------------------------------- - ------------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------ - ------------------------------------ + ----------------------------------- + --------------------------------- - ---------------------------------- + ---------------------------------- - ----------------------------------- + ----------------------------------- - ---------------------------------- + ---------------------------------- - --------------------------------- does not converge on {0, Infinity}.
                                           17/2   7             29/2                     17/2   7             29/2                     17/2   7             29/2                     17/2   7             29/2                      17/2   7             29/2                      17/2   7             29/2                     17/2   7             29/2                    17/2   7             29/2                 13/2   7             25/2                 13/2   7             25/2                  13/2   7             25/2                  13/2   7             25/2                  13/2   7             25/2                  13/2   7             25/2                 13/2   7             25/2                 13/2   7             25/2               9/2   7             21/2                9/2   7             21/2                9/2   7             21/2                9/2   7             21/2                 9/2   7             21/2                 9/2   7             21/2                9/2   7             21/2               9/2   7             21/2             5/2   7             17/2             5/2   7             17/2               5/2   7             17/2               5/2   7             17/2               5/2   7             17/2               5/2   7             17/2              5/2   7             17/2              5/2   7             17/2                           7  13/2                                    7  13/2                                     7  13/2                                      7  13/2                                      7  13/2                                      7  13/2                                      7  13/2                                    7  13/2                             19/2   7             31/2                      19/2   7             31/2                       19/2   7             31/2                       19/2   7             31/2                       19/2   7             31/2                       19/2   7             31/2                      19/2   7             31/2                      19/2   7             31/2                   15/2   7             27/2                   15/2   7             27/2                   15/2   7             27/2                   15/2   7             27/2                   15/2   7             27/2                   15/2   7             27/2                   15/2   7             27/2                  15/2   7             27/2                11/2   7             23/2               11/2   7             23/2                11/2   7             23/2                 11/2   7             23/2                 11/2   7             23/2                11/2   7             23/2                11/2   7             23/2                11/2   7             23/2             7/2   7             19/2              7/2   7             19/2               7/2   7             19/2                7/2   7             19/2                7/2   7             19/2               7/2   7             19/2               7/2   7             19/2               7/2   7             19/2            3/2   7             15/2            3/2   7             15/2             3/2   7             15/2              3/2   7             15/2              3/2   7             15/2             3/2   7             15/2             3/2   7             15/2             3/2   7             15/2
                               1073741824 k     k0  Sqrt[2 Pi] x             1073741824 k     k0  Sqrt[2 Pi] x             1073741824 k     k0  Sqrt[2 Pi] x             1073741824 k     k0  Sqrt[2 Pi] x              1073741824 k     k0  Sqrt[2 Pi] x              1073741824 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             2097152 k     k0  Sqrt[2 Pi] x             2097152 k     k0  Sqrt[2 Pi] x             2097152 k     k0  Sqrt[2 Pi] x             2097152 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             16384 k    k0  Sqrt[2 Pi] x             16384 k    k0  Sqrt[2 Pi] x              16384 k    k0  Sqrt[2 Pi] x              16384 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               64 k    k0  Sqrt[2 Pi] x               64 k    k0  Sqrt[2 Pi] x               64 k    k0  Sqrt[2 Pi] x               64 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                                Sqrt[k] k0  x                              Sqrt[k] k0  x                     8589934592 k     k0  Sqrt[2 Pi] x              8589934592 k     k0  Sqrt[2 Pi] x               8589934592 k     k0  Sqrt[2 Pi] x               8589934592 k     k0  Sqrt[2 Pi] x               8589934592 k     k0  Sqrt[2 Pi] x               8589934592 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             16777216 k     k0  Sqrt[2 Pi] x             16777216 k     k0  Sqrt[2 Pi] x             16777216 k     k0  Sqrt[2 Pi] x             16777216 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            131072 k     k0  Sqrt[2 Pi] x             131072 k     k0  Sqrt[2 Pi] x             131072 k     k0  Sqrt[2 Pi] x            131072 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              512 k    k0  Sqrt[2 Pi] x               512 k    k0  Sqrt[2 Pi] x               512 k    k0  Sqrt[2 Pi] x              512 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              4 k    k0  Sqrt[2 Pi] x               4 k    k0  Sqrt[2 Pi] x               4 k    k0  Sqrt[2 Pi] x              4 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)))^7*BesselJ[3, k*x])/(k0^7*x^6), {x, 0, Infinity}, Assumptions -> n == 3 && q == 7 && κ == 7 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]