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Bessel transform mathematica results etc. Former-commit-id: 3dca9d0ccbfefa4c5f3867ce4ba31229646ca2d9
2018-01-15 15:14:15 +02:00
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}]