qpms/besseltransforms/klarge/5-1-3

((-5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(c - I*k0)^2]) + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(2*c - I*k0)^2]) - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/(k^3*Sqrt[1 + k^2/(4*c - I*k0)^2]) - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/(k^3*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (k^3 - 4*k*k0^2 + (I*k*k0*(3*k^2 - 4*k0^2))/Sqrt[k^2 - k0^2])/k^4)/k0
((-5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))*Power(c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))) + (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))*Power(2*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))) - (10*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))*Power(3*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))) + (5*(Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))*Power(4*c - Complex(0,1)*k0,2)))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))) - (Power(k,2)*(-3 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + 4*(-1 + Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2)))*Power(5*c - Complex(0,1)*k0,2))/(Power(k,3)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Power(k,3) - 4*k*Power(k0,2) + (Complex(0,1)*k*k0*(3*Power(k,2) - 4*Power(k0,2)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,4))/k0
SeriesData[k, Infinity, {-(1/(k*k0)), (k - (3*I)*k0)/(k*k0), (I*(3*k - (4*I)*k0))/k, (-8*k*k0 + (5*I)*k0^2)/(2*k), ((3*(5*c - I*k0)^4)/(8*k) - (5*I)/2*k0^3 - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*((-3*(c - I*k0)^4)/(8*k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*((-3*(2*c - I*k0)^4)/(8*k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*((-3*(3*c - I*k0)^4)/(8*k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*((-3*(4*c - I*k0)^4)/(8*k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, ((-2*(5*c - I*k0)^5)/k + (9*(5*c - I*k0)^4*((5*c)/k - (I*k0)/k))/8 - 5*((2*(c - I*k0)^5)/k - (9*(c - I*k0)^4*(c/k - (I*k0)/k))/8) + 10*((2*(2*c - I*k0)^5)/k - (9*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/8) - 10*((2*(3*c - I*k0)^5)/k - (9*(3*c - I*k0)^4*((3*c)/k - (I*k0)/k))/8) + 5*((2*(4*c - I*k0)^5)/k - (9*(4*c - I*k0)^4*((4*c)/k - (I*k0)/k))/8))/k0, ((11*(5*c - I*k0)^6)/(8*k) - (7*I)/8*k0^5 - (11*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/8 - 5*((-11*(c - I*k0)^6)/(8*k) + (11*(c - I*k0)^5*(c/k - (I*k0)/k))/8) + 10*((-11*(2*c - I*k0)^6)/(8*k) + (11*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/8) - 10*((-11*(3*c - I*k0)^6)/(8*k) + (11*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/8) + 5*((-11*(4*c - I*k0)^6)/(8*k) + (11*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/8))/k0, ((45*(c - I*k0)^6*(c/k - (I*k0)/k))/16 - (45*(2*c - I*k0)^6*((2*c)/k - (I*k0)/k))/8 + (45*(3*c - I*k0)^6*((3*c)/k - (I*k0)/k))/8 - (45*(4*c - I*k0)^6*((4*c)/k - (I*k0)/k))/16 + (9*(5*c - I*k0)^6*((5*c)/k - (I*k0)/k))/16)/k0, ((-55*(5*c - I*k0)^8)/(128*k) - (9*I)/16*k0^7 + (55*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((55*(c - I*k0)^8)/(128*k) - (55*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((55*(2*c - I*k0)^8)/(128*k) - (55*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((55*(3*c - I*k0)^8)/(128*k) - (55*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((55*(4*c - I*k0)^8)/(128*k) - (55*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, ((-275*(c - I*k0)^8*(c/k - (I*k0)/k))/128 + (275*(2*c - I*k0)^8*((2*c)/k - (I*k0)/k))/64 - (275*(3*c - I*k0)^8*((3*c)/k - (I*k0)/k))/64 + (275*(4*c - I*k0)^8*((4*c)/k - (I*k0)/k))/128 - (55*(5*c - I*k0)^8*((5*c)/k - (I*k0)/k))/128)/k0, ((15*(5*c - I*k0)^10)/(64*k) - (55*I)/128*k0^9 - (15*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/64 - 5*((-15*(c - I*k0)^10)/(64*k) + (15*(c - I*k0)^9*(c/k - (I*k0)/k))/64) + 10*((-15*(2*c - I*k0)^10)/(64*k) + (15*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/64) - 10*((-15*(3*c - I*k0)^10)/(64*k) + (15*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/64) + 5*((-15*(4*c - I*k0)^10)/(64*k) + (15*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1]
(k^2 - (5*(k^2*(-3 + Sqrt[1 + k^2/(c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(c - I*k0)^2])*(c - I*k0)^2))/Sqrt[1 + k^2/(c - I*k0)^2] + (10*(k^2*(-3 + Sqrt[1 + k^2/(2*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(2*c - I*k0)^2])*(2*c - I*k0)^2))/Sqrt[1 + k^2/(2*c - I*k0)^2] - (10*(k^2*(-3 + Sqrt[1 + k^2/(3*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(3*c - I*k0)^2])*(3*c - I*k0)^2))/Sqrt[1 + k^2/(3*c - I*k0)^2] + (5*(k^2*(-3 + Sqrt[1 + k^2/(4*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(4*c - I*k0)^2])*(4*c - I*k0)^2))/Sqrt[1 + k^2/(4*c - I*k0)^2] - (k^2*(-3 + Sqrt[1 + k^2/(5*c - I*k0)^2]) + 4*(-1 + Sqrt[1 + k^2/(5*c - I*k0)^2])*(5*c - I*k0)^2)/Sqrt[1 + k^2/(5*c - I*k0)^2] - 4*k0^2 + (I*k0*(3*k^2 - 4*k0^2))/Sqrt[k^2 - k0^2])/(k^3*k0)
Další Hankelovy transformace pro kappa=5 Former-commit-id: cc20e7f5dbf8651a81543f84ac066d011e84082b 2018-01-23 00:52:10 +02:00			((-5(k^2(-3 + Sqrt[1 + k^2/(c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2))/(k^3Sqrt[1 + k^2/(c - Ik0)^2]) + (10(k^2(-3 + Sqrt[1 + k^2/(2c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2))/(k^3Sqrt[1 + k^2/(2c - Ik0)^2]) - (10(k^2(-3 + Sqrt[1 + k^2/(3c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2))/(k^3Sqrt[1 + k^2/(3c - Ik0)^2]) + (5(k^2(-3 + Sqrt[1 + k^2/(4c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2))/(k^3Sqrt[1 + k^2/(4c - Ik0)^2]) - (k^2(-3 + Sqrt[1 + k^2/(5c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2)/(k^3Sqrt[1 + k^2/(5c - Ik0)^2]) + (k^3 - 4kk0^2 + (Ikk0(3k^2 - 4*k0^2))/Sqrt[k^2 - k0^2])/k^4)/k0
			((-5(Power(k,2)(-3 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2))) + 4(-1 + Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))Power(c - Complex(0,1)k0,2)))/(Power(k,3)Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2))) + (10(Power(k,2)(-3 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2))) + 4(-1 + Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))Power(2c - Complex(0,1)k0,2)))/(Power(k,3)Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2))) - (10(Power(k,2)(-3 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2))) + 4(-1 + Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))Power(3c - Complex(0,1)k0,2)))/(Power(k,3)Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2))) + (5(Power(k,2)(-3 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2))) + 4(-1 + Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))Power(4c - Complex(0,1)k0,2)))/(Power(k,3)Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2))) - (Power(k,2)(-3 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2))) + 4(-1 + Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2)))Power(5c - Complex(0,1)k0,2))/(Power(k,3)Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2))) + (Power(k,3) - 4kPower(k0,2) + (Complex(0,1)kk0(3Power(k,2) - 4*Power(k0,2)))/Sqrt(Power(k,2) - Power(k0,2)))/Power(k,4))/k0
			SeriesData[k, Infinity, {-(1/(kk0)), (k - (3I)k0)/(kk0), (I(3k - (4I)k0))/k, (-8kk0 + (5I)k0^2)/(2k), ((3(5c - Ik0)^4)/(8k) - (5I)/2k0^3 - (3(5c - Ik0)^3((5c)/k - (Ik0)/k))/8 - 5((-3(c - Ik0)^4)/(8k) + (3(c - Ik0)^3(c/k - (Ik0)/k))/8) + 10((-3(2c - Ik0)^4)/(8k) + (3(2c - Ik0)^3((2c)/k - (Ik0)/k))/8) - 10((-3(3c - Ik0)^4)/(8k) + (3(3c - Ik0)^3((3c)/k - (Ik0)/k))/8) + 5((-3(4c - Ik0)^4)/(8k) + (3(4c - Ik0)^3((4c)/k - (Ik0)/k))/8))/k0, ((-2(5c - Ik0)^5)/k + (9(5c - Ik0)^4((5c)/k - (Ik0)/k))/8 - 5((2(c - Ik0)^5)/k - (9(c - Ik0)^4(c/k - (Ik0)/k))/8) + 10((2(2c - Ik0)^5)/k - (9(2c - Ik0)^4((2c)/k - (Ik0)/k))/8) - 10((2(3c - Ik0)^5)/k - (9(3c - Ik0)^4((3c)/k - (Ik0)/k))/8) + 5((2(4c - Ik0)^5)/k - (9(4c - Ik0)^4((4c)/k - (Ik0)/k))/8))/k0, ((11(5c - Ik0)^6)/(8k) - (7I)/8k0^5 - (11(5c - Ik0)^5((5c)/k - (Ik0)/k))/8 - 5((-11(c - Ik0)^6)/(8k) + (11(c - Ik0)^5(c/k - (Ik0)/k))/8) + 10((-11(2c - Ik0)^6)/(8k) + (11(2c - Ik0)^5((2c)/k - (Ik0)/k))/8) - 10((-11(3c - Ik0)^6)/(8k) + (11(3c - Ik0)^5((3c)/k - (Ik0)/k))/8) + 5((-11(4c - Ik0)^6)/(8k) + (11(4c - Ik0)^5((4c)/k - (Ik0)/k))/8))/k0, ((45(c - Ik0)^6(c/k - (Ik0)/k))/16 - (45(2c - Ik0)^6((2c)/k - (Ik0)/k))/8 + (45(3c - Ik0)^6((3c)/k - (Ik0)/k))/8 - (45(4c - Ik0)^6((4c)/k - (Ik0)/k))/16 + (9(5c - Ik0)^6((5c)/k - (Ik0)/k))/16)/k0, ((-55(5c - Ik0)^8)/(128k) - (9I)/16k0^7 + (55(5c - Ik0)^7((5c)/k - (Ik0)/k))/128 - 5((55(c - Ik0)^8)/(128k) - (55(c - Ik0)^7(c/k - (Ik0)/k))/128) + 10((55(2c - Ik0)^8)/(128k) - (55(2c - Ik0)^7((2c)/k - (Ik0)/k))/128) - 10((55(3c - Ik0)^8)/(128k) - (55(3c - Ik0)^7((3c)/k - (Ik0)/k))/128) + 5((55(4c - Ik0)^8)/(128k) - (55(4c - Ik0)^7((4c)/k - (Ik0)/k))/128))/k0, ((-275(c - Ik0)^8(c/k - (Ik0)/k))/128 + (275(2c - Ik0)^8((2c)/k - (Ik0)/k))/64 - (275(3c - Ik0)^8((3c)/k - (Ik0)/k))/64 + (275(4c - Ik0)^8((4c)/k - (Ik0)/k))/128 - (55(5c - Ik0)^8((5c)/k - (Ik0)/k))/128)/k0, ((15(5c - Ik0)^10)/(64k) - (55I)/128k0^9 - (15(5c - Ik0)^9((5c)/k - (Ik0)/k))/64 - 5((-15(c - Ik0)^10)/(64k) + (15(c - Ik0)^9(c/k - (Ik0)/k))/64) + 10((-15(2c - Ik0)^10)/(64k) + (15(2c - Ik0)^9((2c)/k - (Ik0)/k))/64) - 10((-15(3c - Ik0)^10)/(64k) + (15(3c - Ik0)^9((3c)/k - (Ik0)/k))/64) + 5((-15(4c - Ik0)^10)/(64k) + (15(4c - Ik0)^9((4c)/k - (I*k0)/k))/64))/k0}, 0, 11, 1]
			(k^2 - (5(k^2(-3 + Sqrt[1 + k^2/(c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(c - Ik0)^2])(c - Ik0)^2))/Sqrt[1 + k^2/(c - Ik0)^2] + (10(k^2(-3 + Sqrt[1 + k^2/(2c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(2c - Ik0)^2])(2c - Ik0)^2))/Sqrt[1 + k^2/(2c - Ik0)^2] - (10(k^2(-3 + Sqrt[1 + k^2/(3c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(3c - Ik0)^2])(3c - Ik0)^2))/Sqrt[1 + k^2/(3c - Ik0)^2] + (5(k^2(-3 + Sqrt[1 + k^2/(4c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(4c - Ik0)^2])(4c - Ik0)^2))/Sqrt[1 + k^2/(4c - Ik0)^2] - (k^2(-3 + Sqrt[1 + k^2/(5c - Ik0)^2]) + 4(-1 + Sqrt[1 + k^2/(5c - Ik0)^2])(5c - Ik0)^2)/Sqrt[1 + k^2/(5c - Ik0)^2] - 4k0^2 + (Ik0(3k^2 - 4k0^2))/Sqrt[k^2 - k0^2])/(k^3*k0)