qpms/besseltransforms/6-4-0

Integrate[(E^(-(c*x) + I*k0*x)*(1 - E^(-(c*x)))^6*BesselJ[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && 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
                             13043905875 E                Cos[-- - k x]   39131717625 E                Cos[-- - k x]   195658588125 E                Cos[-- - k x]   65219529375 E                Cos[-- - k x]   195658588125 E                Cos[-- - k x]   39131717625 E                Cos[-- - k x]   13043905875 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   7203735 E                Cos[-- - k x]   36018675 E                Cos[-- - k x]   12006225 E                Cos[-- - k x]   36018675 E                Cos[-- - k x]   7203735 E                Cos[-- - k x]   2401245 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   11025 E                Cos[-- - k x]   55125 E                Cos[-- - k x]   18375 E                Cos[-- - k x]   55125 E                Cos[-- - k x]   11025 E                Cos[-- - k x]   3675 E                Cos[-- - k x]   9 E                Cos[-- - k x]   27 E                Cos[-- - k x]   135 E                Cos[-- - k x]   45 E                Cos[-- - k x]   135 E                Cos[-- - k x]   27 E                Cos[-- - k x]   9 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]   418854310875 E                Sin[-- - k x]   1256562932625 E                Sin[-- - k x]   6282814663125 E                Sin[-- - k x]   2094271554375 E                Sin[-- - k x]   6282814663125 E                Sin[-- - k x]   1256562932625 E                Sin[-- - k x]   418854310875 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   173918745 E                Sin[-- - k x]   869593725 E                Sin[-- - k x]   289864575 E                Sin[-- - k x]   869593725 E                Sin[-- - k x]   173918745 E                Sin[-- - k x]   57972915 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   178605 E                Sin[-- - k x]   893025 E                Sin[-- - k x]   297675 E                Sin[-- - k x]   893025 E                Sin[-- - k x]   178605 E                Sin[-- - k x]   59535 E                Sin[-- - k x]   75 E                Sin[-- - k x]   225 E                Sin[-- - k x]   1125 E                Sin[-- - k x]   375 E                Sin[-- - k x]   1125 E                Sin[-- - k x]   225 E                Sin[-- - k x]   75 E                Sin[-- - k x]   E                Sin[-- - k x]   3 E                Sin[-- - k x]   15 E                Sin[-- - k x]   5 E                Sin[-- - k x]   15 E                Sin[-- - k x]   3 E                Sin[-- - k x]   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[0, k*x])/(k0^4*x^3), {x, 0, Infinity}, Assumptions -> n == 0 && q == 4 && κ == 6 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0], {k, Infinity, 10}]