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qpms/besseltransforms/ksmall/5-3-1

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Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b
2018-01-23 00:52:10 +02:00
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0]
Integrate((Power(E,I*k0*x)*Power(1 - Power(E,-(c*x)),5)*BesselJ(1,k*x))/(Power(k0,3)*Power(x,2)),List(x,0,DirectedInfinity(1)),Rule(Assumptions,n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0))
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 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 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 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 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 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 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 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 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 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
14783093325 E Cos[-- + k x] 14783093325 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 73915466625 E Cos[-- + k x] 2837835 E Cos[-- + k x] 2837835 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 14189175 E Cos[-- + k x] 4725 E Cos[-- + k x] 4725 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 23625 E Cos[-- + k x] 15 E Cos[-- + k x] 15 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] 75 E Cos[-- + k x] E Sqrt[--] Cos[-- + k x] E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 10 E Sqrt[--] Cos[-- + k x] 5 E Sqrt[--] Cos[-- + k x] 468131288625 E Sin[-- + k x] 468131288625 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 2340656443125 E Sin[-- + k x] 66891825 E Sin[-- + k x] 66891825 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 334459125 E Sin[-- + k x] 72765 E Sin[-- + k x] 72765 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 363825 E Sin[-- + k x] 105 E Sin[-- + k x] 105 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 525 E Sin[-- + k x] 3 E Sin[-- + k x] 3 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 E Sin[-- + k x] 15 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 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
Integrate::idiv: Integral of ------------------------------------- - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ + ------------------------------------------ - ------------------------------------------ - ---------------------------------- + -------------------------------------- - --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ------------------------------- - ----------------------------------- + ------------------------------------ - ------------------------------------ + ------------------------------------ - ------------------------------------ - --------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - ------------------------------ + --------------------------------------- - ----------------------------------------- + ------------------------------------------ - ------------------------------------------ + ----------------------------------------- + ------------------------------------- - ------------------------------------------- + -------------------------------------------- - -------------------------------------------- + -------------------------------------------- - -------------------------------------------- - ----------------------------------- + --------------------------------------- - ---------------------------------------- + ---------------------------------------- - ---------------------------------------- + ---------------------------------------- + --------------------------------- - ------------------------------------ + ------------------------------------- - ------------------------------------- + ------------------------------------- - ------------------------------------- - ----------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- - ---------------------------------- + ---------------------------------- + -------------------------- - -------------------------------- + --------------------------------- - --------------------------------- + --------------------------------- - --------------------------------- does not converge on {0, Infinity}.
17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 17/2 3 21/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 13/2 3 17/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 9/2 3 13/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 5/2 3 9/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 3 5/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 19/2 3 23/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 15/2 3 19/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 11/2 3 15/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 7/2 3 11/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2 3/2 3 7/2
1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 1073741824 k k0 Sqrt[2 Pi] x 536870912 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 2097152 k k0 Sqrt[2 Pi] x 2097152 k k0 Sqrt[2 Pi] x 1048576 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 16384 k k0 Sqrt[2 Pi] x 16384 k k0 Sqrt[2 Pi] x 8192 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 64 k k0 Sqrt[2 Pi] x 64 k k0 Sqrt[2 Pi] x 32 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 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 8589934592 k k0 Sqrt[2 Pi] x 4294967296 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 16777216 k k0 Sqrt[2 Pi] x 16777216 k k0 Sqrt[2 Pi] x 8388608 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 131072 k k0 Sqrt[2 Pi] x 131072 k k0 Sqrt[2 Pi] x 65536 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 512 k k0 Sqrt[2 Pi] x 512 k k0 Sqrt[2 Pi] x 256 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 4 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 2 k k0 Sqrt[2 Pi] x 4 k k0 Sqrt[2 Pi] x
Series[Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5 && c >= 0 && k >= 0 && k0 >= 0 && n >= 0 && k < k0], {k, Infinity, 10}]
Integrate[(E^(I*k0*x)*(1 - E^(-(c*x)))^5*BesselJ[1, k*x])/(k0^3*x^2), {x, 0, Infinity}, Assumptions -> n == 1 && q == 3 && κ == 5]