qpms/besseltransforms/ksmall/5-5-5

(-(35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8)/(2688*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8)/(1344*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8)/(1344*k^5) + (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8)/(2688*k^5) - (35*k^8 + 8*k^6*(35 - 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 16*k^4*(35 - 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 64*k^2*(7 - 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 - 128*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8)/(13440*k^5) + (35*k^8 + 16*k^4*k0^3*(35*k0 - 24*Sqrt[-k^2 + k0^2]) + 128*k0^7*(k0 - Sqrt[-k^2 + k0^2]) + 64*k^2*k0^5*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + 8*k^6*k0*(-35*k0 + 16*Sqrt[-k^2 + k0^2]))/(13440*k^5))/k0^5
(-(35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,8))/(2688.*Power(k,5)) + (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,8))/(1344.*Power(k,5)) - (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,8))/(1344.*Power(k,5)) + (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,8))/(2688.*Power(k,5)) - (35*Power(k,8) + 8*Power(k,6)*(35 - 16*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2) + 16*Power(k,4)*(35 - 24*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,4) + 64*Power(k,2)*(7 - 6*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,6) - 128*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,8))/(13440.*Power(k,5)) + (35*Power(k,8) + 16*Power(k,4)*Power(k0,3)*(35*k0 - 24*Sqrt(-Power(k,2) + Power(k0,2))) + 128*Power(k0,7)*(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 64*Power(k,2)*Power(k0,5)*(-7*k0 + 6*Sqrt(-Power(k,2) + Power(k0,2))) + 8*Power(k,6)*k0*(-35*k0 + 16*Sqrt(-Power(k,2) + Power(k0,2))))/(13440.*Power(k,5)))/Power(k0,5)
SeriesData[k, Infinity, {(5*c^5)/k0^5, (-60*c^6)/k0^5 + ((24*I)*c^5)/k0^4, (35*(20*c^7 - (15*I)*c^6*k0 - 3*c^5*k0^2))/(2*k0^5), (-1200*c^8)/k0^5 + ((1280*I)*c^7)/k0^4 + (480*c^6)/k0^3 - ((64*I)*c^5)/k0^2, (105*(331*c^9 - (450*I)*c^8*k0 - 240*c^7*k0^2 + (60*I)*c^6*k0^3 + 6*c^5*k0^4))/(16*k0^5), 0, (-11*(22430*c^11 - (42525*I)*c^10*k0 - 34755*c^9*k0^2 + (15750*I)*c^8*k0^3 + 4200*c^7*k0^4 - (630*I)*c^6*k0^5 - 42*c^5*k0^6))/(32*k0^5), 0, (143*(52507*c^13 - (125400*I)*c^12*k0 - 134580*c^11*k0^2 + (85050*I)*c^10*k0^3 + 34755*c^9*k0^4 - (9450*I)*c^8*k0^5 - 1680*c^7*k0^6 + (180*I)*c^6*k0^7 + 9*c^5*k0^8))/(128*k0^5)}, 2, 11, 1]
(5*k^6*(-35 + 16*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2 + 10*k^4*(-35 + 24*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^4 + 40*k^2*(-7 + 6*Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^6 + 80*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^8 + 10*k^6*(35 - 16*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2 + 20*k^4*(35 - 24*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^4 + 80*k^2*(7 - 6*Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^6 - 160*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^8 + 10*k^6*(-35 + 16*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2 + 20*k^4*(-35 + 24*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^4 + 80*k^2*(-7 + 6*Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^6 + 160*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^8 + 5*k^6*(35 - 16*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2 + 10*k^4*(35 - 24*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^4 + 40*k^2*(7 - 6*Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^6 - 80*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^8 + k^6*(-35 + 16*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2 + 2*k^4*(-35 + 24*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^4 + 8*k^2*(-7 + 6*Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^6 + 16*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^8 + 2*k^4*k0^3*(35*k0 - 24*Sqrt[-k^2 + k0^2]) + 16*k0^7*(k0 - Sqrt[-k^2 + k0^2]) + 8*k^2*k0^5*(-7*k0 + 6*Sqrt[-k^2 + k0^2]) + k^6*k0*(-35*k0 + 16*Sqrt[-k^2 + k0^2]))/(1680*k^5*k0^5)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			(-(35k^8 + 8k^6(35 - 16Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 + 16k^4(35 - 24Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4 + 64k^2(7 - 6Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^6 - 128(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^8)/(2688k^5) + (35k^8 + 8k^6(35 - 16Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 + 16k^4(35 - 24Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4 + 64k^2(7 - 6Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^6 - 128(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^8)/(1344k^5) - (35k^8 + 8k^6(35 - 16Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 + 16k^4(35 - 24Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4 + 64k^2(7 - 6Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^6 - 128(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^8)/(1344k^5) + (35k^8 + 8k^6(35 - 16Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 + 16k^4(35 - 24Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4 + 64k^2(7 - 6Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^6 - 128(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^8)/(2688k^5) - (35k^8 + 8k^6(35 - 16Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 + 16k^4(35 - 24Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4 + 64k^2(7 - 6Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^6 - 128(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^8)/(13440k^5) + (35k^8 + 16k^4k0^3(35k0 - 24Sqrt[-k^2 + k0^2]) + 128k0^7(k0 - Sqrt[-k^2 + k0^2]) + 64k^2k0^5(-7k0 + 6Sqrt[-k^2 + k0^2]) + 8k^6k0(-35k0 + 16Sqrt[-k^2 + k0^2]))/(13440*k^5))/k0^5
			(-(35Power(k,8) + 8Power(k,6)(35 - 16Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,2) + 16Power(k,4)(35 - 24Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,4) + 64Power(k,2)(7 - 6Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,6) - 128(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,8))/(2688.Power(k,5)) + (35Power(k,8) + 8Power(k,6)(35 - 16Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,2) + 16Power(k,4)(35 - 24Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,4) + 64Power(k,2)(7 - 6Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,6) - 128(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,8))/(1344.Power(k,5)) - (35Power(k,8) + 8Power(k,6)(35 - 16Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,2) + 16Power(k,4)(35 - 24Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,4) + 64Power(k,2)(7 - 6Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,6) - 128(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,8))/(1344.Power(k,5)) + (35Power(k,8) + 8Power(k,6)(35 - 16Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,2) + 16Power(k,4)(35 - 24Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,4) + 64Power(k,2)(7 - 6Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,6) - 128(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,8))/(2688.Power(k,5)) - (35Power(k,8) + 8Power(k,6)(35 - 16Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,2) + 16Power(k,4)(35 - 24Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,4) + 64Power(k,2)(7 - 6Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,6) - 128(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,8))/(13440.Power(k,5)) + (35Power(k,8) + 16Power(k,4)Power(k0,3)(35k0 - 24Sqrt(-Power(k,2) + Power(k0,2))) + 128Power(k0,7)(k0 - Sqrt(-Power(k,2) + Power(k0,2))) + 64Power(k,2)Power(k0,5)(-7k0 + 6Sqrt(-Power(k,2) + Power(k0,2))) + 8Power(k,6)k0(-35k0 + 16Sqrt(-Power(k,2) + Power(k0,2))))/(13440.*Power(k,5)))/Power(k0,5)
			SeriesData[k, Infinity, {(5c^5)/k0^5, (-60c^6)/k0^5 + ((24I)c^5)/k0^4, (35(20c^7 - (15I)c^6k0 - 3c^5k0^2))/(2k0^5), (-1200c^8)/k0^5 + ((1280I)c^7)/k0^4 + (480c^6)/k0^3 - ((64I)c^5)/k0^2, (105(331c^9 - (450I)c^8k0 - 240c^7k0^2 + (60I)c^6k0^3 + 6c^5k0^4))/(16k0^5), 0, (-11(22430c^11 - (42525I)c^10k0 - 34755c^9k0^2 + (15750I)c^8k0^3 + 4200c^7k0^4 - (630I)c^6k0^5 - 42c^5k0^6))/(32k0^5), 0, (143(52507c^13 - (125400I)c^12k0 - 134580c^11k0^2 + (85050I)c^10k0^3 + 34755c^9k0^4 - (9450I)c^8k0^5 - 1680c^7k0^6 + (180I)c^6k0^7 + 9c^5k0^8))/(128k0^5)}, 2, 11, 1]
			(5k^6(-35 + 16Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2 + 10k^4(-35 + 24Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^4 + 40k^2(-7 + 6Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^6 + 80(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^8 + 10k^6(35 - 16Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2 + 20k^4(35 - 24Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^4 + 80k^2(7 - 6Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^6 - 160(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^8 + 10k^6(-35 + 16Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2 + 20k^4(-35 + 24Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^4 + 80k^2(-7 + 6Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^6 + 160(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^8 + 5k^6(35 - 16Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2 + 10k^4(35 - 24Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^4 + 40k^2(7 - 6Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^6 - 80(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^8 + k^6(-35 + 16Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2 + 2k^4(-35 + 24Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^4 + 8k^2(-7 + 6Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^6 + 16(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^8 + 2k^4k0^3(35k0 - 24Sqrt[-k^2 + k0^2]) + 16k0^7(k0 - Sqrt[-k^2 + k0^2]) + 8k^2k0^5(-7k0 + 6Sqrt[-k^2 + k0^2]) + k^6k0(-35k0 + 16Sqrt[-k^2 + k0^2]))/(1680k^5*k0^5)