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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)))^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}]