qpms/besseltransforms/klarge/5-1-4

((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(k^4*Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(k^4*Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + ((4*I)*k*k0*(k^2 - 2*k0^2) + (k*(k^4 - 8*k^2*k0^2 + 8*k0^4))/Sqrt[k^2 - k0^2])/k^5)/k0
((-5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) + (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (10*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) + (5*(Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4)))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (Power(k,4) - 4*Power(k,2)*(-2 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) - 8*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4))/(Power(k,4)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (Complex(0,4)*k*k0*(Power(k,2) - 2*Power(k0,2)) + (k*(Power(k,4) - 8*Power(k,2)*Power(k0,2) + 8*Power(k0,4)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,5))/k0
SeriesData[k, Infinity, {-(1/(k*k0)), (k - (4*I)*k0)/(k*k0), (I/2*(8*k - (15*I)*k0))/k, (-15*k*k0 + (16*I)*k0^2)/(2*k), ((-8*I)*k0^3 - (5*((4*(c - I*k0)^5)/k + (3*(c - I*k0)^4*(c/k - (I*k0)/k))/8))/(c - I*k0) + (10*((4*(2*c - I*k0)^5)/k + (3*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8))/(2*c - I*k0) - (10*((4*(3*c - I*k0)^5)/k + (3*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8))/(3*c - I*k0) + (5*((4*(4*c - I*k0)^5)/k + (3*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/(4*c - I*k0) + ((-4*(5*c - I*k0)^5)/k - (3*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8)/(5*c - I*k0))/k0, ((35*k0^4)/8 - (5*((3*(c - I*k0)^6)/(2*k) - (3*(c - I*k0)^5*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((3*(2*c - I*k0)^6)/(2*k) - (3*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((3*(3*c - I*k0)^6)/(2*k) - (3*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((3*(4*c - I*k0)^6)/(2*k) - (3*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-3*(5*c - I*k0)^6)/(2*k) + (3*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-5*((-4*(c - I*k0)^7)/k + (43*(c - I*k0)^6*(c/k - (I*k0)/k))/16))/(c - I*k0) + (10*((-4*(2*c - I*k0)^7)/k + (43*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/16))/(2*c - I*k0) - (10*((-4*(3*c - I*k0)^7)/k + (43*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/16))/(3*c - I*k0) + (5*((-4*(4*c - I*k0)^7)/k + (43*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16))/(4*c - I*k0) + ((4*(5*c - I*k0)^7)/k - (43*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/(5*c - I*k0))/k0, ((21*k0^6)/16 - (5*((5*(c - I*k0)^8)/(2*k) - (5*(c - I*k0)^7*(c/k - (I*k0)/k))/2))/(c - I*k0) + (10*((5*(2*c - I*k0)^8)/(2*k) - (5*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/2))/(2*c - I*k0) - (10*((5*(3*c - I*k0)^8)/(2*k) - (5*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/2))/(3*c - I*k0) + (5*((5*(4*c - I*k0)^8)/(2*k) - (5*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/2))/(4*c - I*k0) + ((-5*(5*c - I*k0)^8)/(2*k) + (5*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/2)/(5*c - I*k0))/k0, ((-495*(c - I*k0)^7*(c/k - (I*k0)/k))/128 + (495*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/64 - (495*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/64 + (495*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128 - (99*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128)/k0, ((99*k0^8)/128 - (5*((-23*(c - I*k0)^10)/(32*k) + (23*(c - I*k0)^9*(c/k - (I*k0)/k))/32))/(c - I*k0) + (10*((-23*(2*c - I*k0)^10)/(32*k) + (23*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/32))/(2*c - I*k0) - (10*((-23*(3*c - I*k0)^10)/(32*k) + (23*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/32))/(3*c - I*k0) + (5*((-23*(4*c - I*k0)^10)/(32*k) + (23*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/32))/(4*c - I*k0) + ((23*(5*c - I*k0)^10)/(32*k) - (23*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/32)/(5*c - I*k0))/k0, ((715*(c - I*k0)^9*(c/k - (I*k0)/k))/256 - (715*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/128 + (715*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/128 - (715*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256 + (143*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256)/k0}, 0, 11, 1]
((-5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4))/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4))/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (10*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4))/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (5*(k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4))/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (k^4 - 4*k^2*(-2 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 - 8*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4)/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (4*I)*k0*(k^2 - 2*k0^2) + (k^4 - 8*k^2*k0^2 + 8*k0^4)/Sqrt[k^2 - k0^2])/(k^4*k0)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			((-5(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4))/(k^4Sqrt[1 + k^2/(c - Ik0)^2](c - Ik0)) + (10(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4))/(k^4Sqrt[1 + k^2/(2c - Ik0)^2](2c - Ik0)) - (10(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4))/(k^4Sqrt[1 + k^2/(3c - Ik0)^2](3c - Ik0)) + (5(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4))/(k^4Sqrt[1 + k^2/(4c - Ik0)^2](4c - Ik0)) - (k^4 - 4k^2(-2 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4)/(k^4Sqrt[1 + k^2/(5c - Ik0)^2](5c - Ik0)) + ((4I)kk0(k^2 - 2k0^2) + (k(k^4 - 8k^2k0^2 + 8k0^4))/Sqrt[k^2 - k0^2])/k^5)/k0
			((-5(Power(k,4) - 4Power(k,2)(-2 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,2) - 8(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,4)))/(Power(k,4)Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2))(c - Complex(0,1)k0)) + (10(Power(k,4) - 4Power(k,2)(-2 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,2) - 8(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,4)))/(Power(k,4)Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2))(2c - Complex(0,1)k0)) - (10(Power(k,4) - 4Power(k,2)(-2 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,2) - 8(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,4)))/(Power(k,4)Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2))(3c - Complex(0,1)k0)) + (5(Power(k,4) - 4Power(k,2)(-2 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,2) - 8(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,4)))/(Power(k,4)Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2))(4c - Complex(0,1)k0)) - (Power(k,4) - 4Power(k,2)(-2 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,2) - 8(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,4))/(Power(k,4)Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2))(5c - Complex(0,1)k0)) + (Complex(0,4)kk0(Power(k,2) - 2Power(k0,2)) + (k(Power(k,4) - 8Power(k,2)Power(k0,2) + 8*Power(k0,4)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,5))/k0
			SeriesData[k, Infinity, {-(1/(kk0)), (k - (4I)k0)/(kk0), (I/2(8k - (15I)k0))/k, (-15kk0 + (16I)k0^2)/(2k), ((-8I)k0^3 - (5((4(c - Ik0)^5)/k + (3(c - Ik0)^4(c/k - (Ik0)/k))/8))/(c - Ik0) + (10((4(2c - Ik0)^5)/k + (3(2c - Ik0)^4((2c)/k - (Ik0)/k))/8))/(2c - Ik0) - (10((4(3c - Ik0)^5)/k + (3(3c - Ik0)^4((3c)/k - (Ik0)/k))/8))/(3c - Ik0) + (5((4(4c - Ik0)^5)/k + (3(4c - Ik0)^4((4c)/k - (Ik0)/k))/8))/(4c - Ik0) + ((-4(5c - Ik0)^5)/k - (3(5c - Ik0)^4((5c)/k - (Ik0)/k))/8)/(5c - Ik0))/k0, ((35k0^4)/8 - (5((3(c - Ik0)^6)/(2k) - (3(c - Ik0)^5(c/k - (Ik0)/k))/2))/(c - Ik0) + (10((3(2c - Ik0)^6)/(2k) - (3(2c - Ik0)^5((2c)/k - (Ik0)/k))/2))/(2c - Ik0) - (10((3(3c - Ik0)^6)/(2k) - (3(3c - Ik0)^5((3c)/k - (Ik0)/k))/2))/(3c - Ik0) + (5((3(4c - Ik0)^6)/(2k) - (3(4c - Ik0)^5((4c)/k - (Ik0)/k))/2))/(4c - Ik0) + ((-3(5c - Ik0)^6)/(2k) + (3(5c - Ik0)^5((5c)/k - (Ik0)/k))/2)/(5c - Ik0))/k0, ((-5((-4(c - Ik0)^7)/k + (43(c - Ik0)^6(c/k - (Ik0)/k))/16))/(c - Ik0) + (10((-4(2c - Ik0)^7)/k + (43(2c - Ik0)^6((2c)/k - (Ik0)/k))/16))/(2c - Ik0) - (10((-4(3c - Ik0)^7)/k + (43(3c - Ik0)^6((3c)/k - (Ik0)/k))/16))/(3c - Ik0) + (5((-4(4c - Ik0)^7)/k + (43(4c - Ik0)^6((4c)/k - (Ik0)/k))/16))/(4c - Ik0) + ((4(5c - Ik0)^7)/k - (43(5c - Ik0)^6((5c)/k - (Ik0)/k))/16)/(5c - Ik0))/k0, ((21k0^6)/16 - (5((5(c - Ik0)^8)/(2k) - (5(c - Ik0)^7(c/k - (Ik0)/k))/2))/(c - Ik0) + (10((5(2c - Ik0)^8)/(2k) - (5(2c - Ik0)^7((2c)/k - (Ik0)/k))/2))/(2c - Ik0) - (10((5(3c - Ik0)^8)/(2k) - (5(3c - Ik0)^7((3c)/k - (Ik0)/k))/2))/(3c - Ik0) + (5((5(4c - Ik0)^8)/(2k) - (5(4c - Ik0)^7((4c)/k - (Ik0)/k))/2))/(4c - Ik0) + ((-5(5c - Ik0)^8)/(2k) + (5(5c - Ik0)^7((5c)/k - (Ik0)/k))/2)/(5c - Ik0))/k0, ((-495(c - Ik0)^7(c/k - (Ik0)/k))/128 + (495(2c - Ik0)^7((2c)/k - (Ik0)/k))/64 - (495(3c - Ik0)^7((3c)/k - (Ik0)/k))/64 + (495(4c - Ik0)^7((4c)/k - (Ik0)/k))/128 - (99(5c - Ik0)^7((5c)/k - (Ik0)/k))/128)/k0, ((99k0^8)/128 - (5((-23(c - Ik0)^10)/(32k) + (23(c - Ik0)^9(c/k - (Ik0)/k))/32))/(c - Ik0) + (10((-23(2c - Ik0)^10)/(32k) + (23(2c - Ik0)^9((2c)/k - (Ik0)/k))/32))/(2c - Ik0) - (10((-23(3c - Ik0)^10)/(32k) + (23(3c - Ik0)^9((3c)/k - (Ik0)/k))/32))/(3c - Ik0) + (5((-23(4c - Ik0)^10)/(32k) + (23(4c - Ik0)^9((4c)/k - (Ik0)/k))/32))/(4c - Ik0) + ((23(5c - Ik0)^10)/(32k) - (23(5c - Ik0)^9((5c)/k - (Ik0)/k))/32)/(5c - Ik0))/k0, ((715(c - Ik0)^9(c/k - (Ik0)/k))/256 - (715(2c - Ik0)^9((2c)/k - (Ik0)/k))/128 + (715(3c - Ik0)^9((3c)/k - (Ik0)/k))/128 - (715(4c - Ik0)^9((4c)/k - (Ik0)/k))/256 + (143(5c - Ik0)^9((5c)/k - (Ik0)/k))/256)/k0}, 0, 11, 1]
			((-5(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4))/(Sqrt[1 + k^2/(c - Ik0)^2](c - Ik0)) + (10(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4))/(Sqrt[1 + k^2/(2c - Ik0)^2](2c - Ik0)) - (10(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4))/(Sqrt[1 + k^2/(3c - Ik0)^2](3c - Ik0)) + (5(k^4 - 4k^2(-2 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4))/(Sqrt[1 + k^2/(4c - Ik0)^2](4c - Ik0)) - (k^4 - 4k^2(-2 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 - 8(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4)/(Sqrt[1 + k^2/(5c - Ik0)^2](5c - Ik0)) + (4I)k0(k^2 - 2k0^2) + (k^4 - 8k^2k0^2 + 8k0^4)/Sqrt[k^2 - k0^2])/(k^4k0)