qpms/besseltransforms/ksmall/5-1-2

(-5*(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2])) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) - (2*(2*c - I*k0))/k^2 + (2*(2*c - I*k0))/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2])) - 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) - (2*(3*c - I*k0))/k^2 + (2*(3*c - I*k0))/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) - (2*(4*c - I*k0))/k^2 + (2*(4*c - I*k0))/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2])) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (2*(5*c - I*k0))/k^2 - (2*(5*c - I*k0))/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (I*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0
(-5*(1/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2))*(c - Complex(0,1)*k0)) - (2*(c - Complex(0,1)*k0))/Power(k,2) + (2*(c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)*k0,2)))) + 10*(1/(Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2))*(2*c - Complex(0,1)*k0)) - (2*(2*c - Complex(0,1)*k0))/Power(k,2) + (2*(2*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(2*c - Complex(0,1)*k0,2)))) - 10*(1/(Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2))*(3*c - Complex(0,1)*k0)) - (2*(3*c - Complex(0,1)*k0))/Power(k,2) + (2*(3*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(3*c - Complex(0,1)*k0,2)))) + 5*(1/(Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2))*(4*c - Complex(0,1)*k0)) - (2*(4*c - Complex(0,1)*k0))/Power(k,2) + (2*(4*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(4*c - Complex(0,1)*k0,2)))) - 1/(Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))*(5*c - Complex(0,1)*k0)) + (2*(5*c - Complex(0,1)*k0))/Power(k,2) - (2*(5*c - Complex(0,1)*k0))/(Power(k,2)*Sqrt(1 + Power(k,2)/Power(5*c - Complex(0,1)*k0,2))) + (Complex(0,1)*(Power(k,2) + 2*k0*(-k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/(Power(k,2)*Sqrt(-Power(k,2) + Power(k0,2))))/k0
SeriesData[k, Infinity, {-(1/(k*k0)), k0^(-1), (3*k0)/(2*k), (-3*k0)/2, ((5*c - I*k0)^4/k - (3*(5*c - I*k0)^3*((5*c)/k - (I*k0)/k))/8 - 5*(-((c - I*k0)^4/k) + (3*(c - I*k0)^3*(c/k - (I*k0)/k))/8) + 10*(-((2*c - I*k0)^4/k) + (3*(2*c - I*k0)^3*((2*c)/k - (I*k0)/k))/8) - 10*(-((3*c - I*k0)^4/k) + (3*(3*c - I*k0)^3*((3*c)/k - (I*k0)/k))/8) + 5*(-((4*c - I*k0)^4/k) + (3*(4*c - I*k0)^3*((4*c)/k - (I*k0)/k))/8))/k0, (-5*k0^3)/8, ((-3*(5*c - I*k0)^6)/(4*k) + (5*(5*c - I*k0)^5*((5*c)/k - (I*k0)/k))/16 - 5*((3*(c - I*k0)^6)/(4*k) - (5*(c - I*k0)^5*(c/k - (I*k0)/k))/16) + 10*((3*(2*c - I*k0)^6)/(4*k) - (5*(2*c - I*k0)^5*((2*c)/k - (I*k0)/k))/16) - 10*((3*(3*c - I*k0)^6)/(4*k) - (5*(3*c - I*k0)^5*((3*c)/k - (I*k0)/k))/16) + 5*((3*(4*c - I*k0)^6)/(4*k) - (5*(4*c - I*k0)^5*((4*c)/k - (I*k0)/k))/16))/k0, (-7*k0^5)/16, ((5*(5*c - I*k0)^8)/(8*k) - (35*(5*c - I*k0)^7*((5*c)/k - (I*k0)/k))/128 - 5*((-5*(c - I*k0)^8)/(8*k) + (35*(c - I*k0)^7*(c/k - (I*k0)/k))/128) + 10*((-5*(2*c - I*k0)^8)/(8*k) + (35*(2*c - I*k0)^7*((2*c)/k - (I*k0)/k))/128) - 10*((-5*(3*c - I*k0)^8)/(8*k) + (35*(3*c - I*k0)^7*((3*c)/k - (I*k0)/k))/128) + 5*((-5*(4*c - I*k0)^8)/(8*k) + (35*(4*c - I*k0)^7*((4*c)/k - (I*k0)/k))/128))/k0, (-45*k0^7)/128, ((-35*(5*c - I*k0)^10)/(64*k) + (63*(5*c - I*k0)^9*((5*c)/k - (I*k0)/k))/256 - 5*((35*(c - I*k0)^10)/(64*k) - (63*(c - I*k0)^9*(c/k - (I*k0)/k))/256) + 10*((35*(2*c - I*k0)^10)/(64*k) - (63*(2*c - I*k0)^9*((2*c)/k - (I*k0)/k))/256) - 10*((35*(3*c - I*k0)^10)/(64*k) - (63*(3*c - I*k0)^9*((3*c)/k - (I*k0)/k))/256) + 5*((35*(4*c - I*k0)^10)/(64*k) - (63*(4*c - I*k0)^9*((4*c)/k - (I*k0)/k))/256))/k0}, 0, 11, 1]
(-5*(1/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) - (2*(c - I*k0))/k^2 + (2*(c - I*k0))/(k^2*Sqrt[1 + k^2/(c - I*k0)^2])) + 5*(1/(Sqrt[1 + k^2/(4*c - I*k0)^2]*(4*c - I*k0)) + (8*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(4*c - I*k0)^2]) + (-8*c + (2*I)*k0)/k^2) - 10*(1/(Sqrt[1 + k^2/(3*c - I*k0)^2]*(3*c - I*k0)) + (6*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(3*c - I*k0)^2]) + (-6*c + (2*I)*k0)/k^2) + 10*(1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (4*c - (2*I)*k0)/(k^2*Sqrt[1 + k^2/(2*c - I*k0)^2]) + (-4*c + (2*I)*k0)/k^2) - 1/(Sqrt[1 + k^2/(5*c - I*k0)^2]*(5*c - I*k0)) + (10*c - (2*I)*k0)/k^2 + (-10*c + (2*I)*k0)/(k^2*Sqrt[1 + k^2/(5*c - I*k0)^2]) + (I*(k^2 + 2*k0*(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0
fixed hankel transform formulae for specific kappa, q, n combinations. Former-commit-id: 6c0dae200188c83aa4fe0b2c37d1585ac192f56c 2018-01-18 17:37:36 +02:00			(-5(1/(Sqrt[1 + k^2/(c - Ik0)^2](c - Ik0)) - (2(c - Ik0))/k^2 + (2(c - Ik0))/(k^2Sqrt[1 + k^2/(c - Ik0)^2])) + 10(1/(Sqrt[1 + k^2/(2c - Ik0)^2](2c - Ik0)) - (2(2c - Ik0))/k^2 + (2(2c - Ik0))/(k^2Sqrt[1 + k^2/(2c - Ik0)^2])) - 10(1/(Sqrt[1 + k^2/(3c - Ik0)^2](3c - Ik0)) - (2(3c - Ik0))/k^2 + (2(3c - Ik0))/(k^2Sqrt[1 + k^2/(3c - Ik0)^2])) + 5(1/(Sqrt[1 + k^2/(4c - Ik0)^2](4c - Ik0)) - (2(4c - Ik0))/k^2 + (2(4c - Ik0))/(k^2Sqrt[1 + k^2/(4c - Ik0)^2])) - 1/(Sqrt[1 + k^2/(5c - Ik0)^2](5c - Ik0)) + (2(5c - Ik0))/k^2 - (2(5c - Ik0))/(k^2Sqrt[1 + k^2/(5c - Ik0)^2]) + (I(k^2 + 2k0(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0
			(-5(1/(Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2))(c - Complex(0,1)k0)) - (2(c - Complex(0,1)k0))/Power(k,2) + (2(c - Complex(0,1)k0))/(Power(k,2)Sqrt(1 + Power(k,2)/Power(c - Complex(0,1)k0,2)))) + 10(1/(Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2))(2c - Complex(0,1)k0)) - (2(2c - Complex(0,1)k0))/Power(k,2) + (2(2c - Complex(0,1)k0))/(Power(k,2)Sqrt(1 + Power(k,2)/Power(2c - Complex(0,1)k0,2)))) - 10(1/(Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2))(3c - Complex(0,1)k0)) - (2(3c - Complex(0,1)k0))/Power(k,2) + (2(3c - Complex(0,1)k0))/(Power(k,2)Sqrt(1 + Power(k,2)/Power(3c - Complex(0,1)k0,2)))) + 5(1/(Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2))(4c - Complex(0,1)k0)) - (2(4c - Complex(0,1)k0))/Power(k,2) + (2(4c - Complex(0,1)k0))/(Power(k,2)Sqrt(1 + Power(k,2)/Power(4c - Complex(0,1)k0,2)))) - 1/(Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2))(5c - Complex(0,1)k0)) + (2(5c - Complex(0,1)k0))/Power(k,2) - (2(5c - Complex(0,1)k0))/(Power(k,2)Sqrt(1 + Power(k,2)/Power(5c - Complex(0,1)k0,2))) + (Complex(0,1)(Power(k,2) + 2k0(-k0 + Sqrt(-Power(k,2) + Power(k0,2)))))/(Power(k,2)*Sqrt(-Power(k,2) + Power(k0,2))))/k0
			SeriesData[k, Infinity, {-(1/(kk0)), k0^(-1), (3k0)/(2k), (-3k0)/2, ((5c - Ik0)^4/k - (3(5c - Ik0)^3((5c)/k - (Ik0)/k))/8 - 5(-((c - Ik0)^4/k) + (3(c - Ik0)^3(c/k - (Ik0)/k))/8) + 10(-((2c - Ik0)^4/k) + (3(2c - Ik0)^3((2c)/k - (Ik0)/k))/8) - 10(-((3c - Ik0)^4/k) + (3(3c - Ik0)^3((3c)/k - (Ik0)/k))/8) + 5(-((4c - Ik0)^4/k) + (3(4c - Ik0)^3((4c)/k - (Ik0)/k))/8))/k0, (-5k0^3)/8, ((-3(5c - Ik0)^6)/(4k) + (5(5c - Ik0)^5((5c)/k - (Ik0)/k))/16 - 5((3(c - Ik0)^6)/(4k) - (5(c - Ik0)^5(c/k - (Ik0)/k))/16) + 10((3(2c - Ik0)^6)/(4k) - (5(2c - Ik0)^5((2c)/k - (Ik0)/k))/16) - 10((3(3c - Ik0)^6)/(4k) - (5(3c - Ik0)^5((3c)/k - (Ik0)/k))/16) + 5((3(4c - Ik0)^6)/(4k) - (5(4c - Ik0)^5((4c)/k - (Ik0)/k))/16))/k0, (-7k0^5)/16, ((5(5c - Ik0)^8)/(8k) - (35(5c - Ik0)^7((5c)/k - (Ik0)/k))/128 - 5((-5(c - Ik0)^8)/(8k) + (35(c - Ik0)^7(c/k - (Ik0)/k))/128) + 10((-5(2c - Ik0)^8)/(8k) + (35(2c - Ik0)^7((2c)/k - (Ik0)/k))/128) - 10((-5(3c - Ik0)^8)/(8k) + (35(3c - Ik0)^7((3c)/k - (Ik0)/k))/128) + 5((-5(4c - Ik0)^8)/(8k) + (35(4c - Ik0)^7((4c)/k - (Ik0)/k))/128))/k0, (-45k0^7)/128, ((-35(5c - Ik0)^10)/(64k) + (63(5c - Ik0)^9((5c)/k - (Ik0)/k))/256 - 5((35(c - Ik0)^10)/(64k) - (63(c - Ik0)^9(c/k - (Ik0)/k))/256) + 10((35(2c - Ik0)^10)/(64k) - (63(2c - Ik0)^9((2c)/k - (Ik0)/k))/256) - 10((35(3c - Ik0)^10)/(64k) - (63(3c - Ik0)^9((3c)/k - (Ik0)/k))/256) + 5((35(4c - Ik0)^10)/(64k) - (63(4c - Ik0)^9((4c)/k - (I*k0)/k))/256))/k0}, 0, 11, 1]
			(-5(1/(Sqrt[1 + k^2/(c - Ik0)^2](c - Ik0)) - (2(c - Ik0))/k^2 + (2(c - Ik0))/(k^2Sqrt[1 + k^2/(c - Ik0)^2])) + 5(1/(Sqrt[1 + k^2/(4c - Ik0)^2](4c - Ik0)) + (8c - (2I)k0)/(k^2Sqrt[1 + k^2/(4c - Ik0)^2]) + (-8c + (2I)k0)/k^2) - 10(1/(Sqrt[1 + k^2/(3c - Ik0)^2](3c - Ik0)) + (6c - (2I)k0)/(k^2Sqrt[1 + k^2/(3c - Ik0)^2]) + (-6c + (2I)k0)/k^2) + 10(1/(Sqrt[1 + k^2/(2c - Ik0)^2](2c - Ik0)) + (4c - (2I)k0)/(k^2Sqrt[1 + k^2/(2c - Ik0)^2]) + (-4c + (2I)k0)/k^2) - 1/(Sqrt[1 + k^2/(5c - Ik0)^2](5c - Ik0)) + (10c - (2I)k0)/k^2 + (-10c + (2I)k0)/(k^2Sqrt[1 + k^2/(5c - Ik0)^2]) + (I(k^2 + 2k0(-k0 + Sqrt[-k^2 + k0^2])))/(k^2*Sqrt[-k^2 + k0^2]))/k0