qpms/besseltransforms/2-1-0

(-2/(Sqrt[1 + k^2/(c - I*k0)^2]*(c - I*k0)) + 1/(Sqrt[1 + k^2/(2*c - I*k0)^2]*(2*c - I*k0)) + (Sqrt[Pi]*(I*Piecewise[{{0, k0^2/k^2 <= 1}}, k/(Sqrt[-k^2 + k0^2]*Sqrt[Pi])] + Piecewise[{{k/(Sqrt[k^2 - k0^2]*Sqrt[Pi]), k0^2/k^2 < 1}}, 0]))/k)/k0
SeriesData[k, Infinity, {-(c^2/(k^2*k0)), 0, (3*(7*c^4 - (12*I)*c^3*k0 - 6*c^2*k0^2))/(4*k^2*k0), 0, (-5*(31*c^6 - (90*I)*c^5*k0 - 105*c^4*k0^2 + (60*I)*c^3*k0^3 + 15*c^2*k0^4))/(8*k^2*k0), 0, (35*(127*c^8 - (504*I)*c^7*k0 - 868*c^6*k0^2 + (840*I)*c^5*k0^3 + 490*c^4*k0^4 - (168*I)*c^3*k0^5 - 28*c^2*k0^6))/(64*k^2*k0), 0, ((((c - I*k0)^3*(2*c - I*k0)^3)/(4*k^2) + ((-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2))*k0^2)/2 + (3*(c - I*k0)*(2*c - I*k0)*k0^4)/(8*k^2) + (3*(c - I*k0)^4*(2*c - I*k0)*(c/k - (I*k0)/k))/(8*k) + (3*(c - I*k0)*(2*c - I*k0)^4*((2*c)/k - (I*k0)/k))/(8*k))*(2*c^2*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0))) - (3*I)*c*((c - I*k0)^5/(16*(2*c - I*k0)) - ((c - I*k0)^3*(2*c - I*k0))/16 - ((c - I*k0)*(2*c - I*k0)^3)/16 + (2*c - I*k0)^5/(16*(c - I*k0)))*k0 + (-(c - I*k0)^5/(16*(2*c - I*k0)) + ((c - I*k0)^3*(2*c - I*k0))/16 + ((c - I*k0)*(2*c - I*k0)^3)/16 - (2*c - I*k0)^5/(16*(c - I*k0)))*k0^2 + c*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - I*k0*((c - I*k0)^5/16 + ((c - I*k0)^3*k0^2)/16 - ((c - I*k0)*k0^4)/16 - k0^6/(16*(c - I*k0))) - 4*c*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0))) + (2*I)*k0*((2*c - I*k0)^5/16 + ((2*c - I*k0)^3*k0^2)/16 - ((2*c - I*k0)*k0^4)/16 - k0^6/(16*(2*c - I*k0)))) + (-((c - I*k0)^3*(2*c - I*k0))/(2*k^2) - ((c - I*k0)*(2*c - I*k0)^3)/(2*k^2) + ((c - I*k0)*(2*c - I*k0)*k0^2)/(2*k^2))*(2*c^2*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0))) - (3*I)*c*((-5*(c - I*k0)^7)/(128*(2*c - I*k0)) + ((c - I*k0)^5*(2*c - I*k0))/32 + ((c - I*k0)^3*(2*c - I*k0)^3)/64 + ((c - I*k0)*(2*c - I*k0)^5)/32 - (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0 + ((5*(c - I*k0)^7)/(128*(2*c - I*k0)) - ((c - I*k0)^5*(2*c - I*k0))/32 - ((c - I*k0)^3*(2*c - I*k0)^3)/64 - ((c - I*k0)*(2*c - I*k0)^5)/32 + (5*(2*c - I*k0)^7)/(128*(c - I*k0)))*k0^2 + c*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) - I*k0*((-5*(c - I*k0)^7)/128 - ((c - I*k0)^5*k0^2)/32 + ((c - I*k0)^3*k0^4)/64 - ((c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(c - I*k0))) - 4*c*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0))) + (2*I)*k0*((-5*(2*c - I*k0)^7)/128 - ((2*c - I*k0)^5*k0^2)/32 + ((2*c - I*k0)^3*k0^4)/64 - ((2*c - I*k0)*k0^6)/32 - (5*k0^8)/(128*(2*c - I*k0)))) + ((c - I*k0)*(2*c - I*k0)*(2*c^2*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0))) - (3*I)*c*((7*(c - I*k0)^9)/(256*(2*c - I*k0)) - (5*(c - I*k0)^7*(2*c - I*k0))/256 - ((c - I*k0)^5*(2*c - I*k0)^3)/128 - ((c - I*k0)^3*(2*c - I*k0)^5)/128 - (5*(c - I*k0)*(2*c - I*k0)^7)/256 + (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0 + ((-7*(c - I*k0)^9)/(256*(2*c - I*k0)) + (5*(c - I*k0)^7*(2*c - I*k0))/256 + ((c - I*k0)^5*(2*c - I*k0)^3)/128 + ((c - I*k0)^3*(2*c - I*k0)^5)/128 + (5*(c - I*k0)*(2*c - I*k0)^7)/256 - (7*(2*c - I*k0)^9)/(256*(c - I*k0)))*k0^2 + c*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) - I*k0*((7*(c - I*k0)^9)/256 + (5*(c - I*k0)^7*k0^2)/256 - ((c - I*k0)^5*k0^4)/128 + ((c - I*k0)^3*k0^6)/128 - (5*(c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(c - I*k0))) - 4*c*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0))) + (2*I)*k0*((7*(2*c - I*k0)^9)/256 + (5*(2*c - I*k0)^7*k0^2)/256 - ((2*c - I*k0)^5*k0^4)/128 + ((2*c - I*k0)^3*k0^6)/128 - (5*(2*c - I*k0)*k0^8)/256 - (7*k0^10)/(256*(2*c - I*k0)))))/k^2 + ((11*c^4 - (24*I)*c^3*k0
Mathematica bessel transforms Former-commit-id: eb38775c75d1c2d5d7a5015bd4a9936108a28d00 2018-03-28 11:52:50 +03:00			`(-2/(Sqrt[1 + k^2/(c - Ik0)^2](c - Ik0)) + 1/(Sqrt[1 + k^2/(2c - Ik0)^2](2c - Ik0)) + (Sqrt[Pi](IPiecewise[{{0, k0^2/k^2 <= 1}}, k/(Sqrt[-k^2 + k0^2]Sqrt[Pi])] + Piecewise[{{k/(Sqrt[k^2 - k0^2]Sqrt[Pi]), k0^2/k^2 < 1}}, 0]))/k)/k0`
			SeriesData[k, Infinity, {-(c^2/(k^2k0)), 0, (3(7c^4 - (12I)c^3k0 - 6c^2k0^2))/(4k^2k0), 0, (-5(31c^6 - (90I)c^5k0 - 105c^4k0^2 + (60I)c^3k0^3 + 15c^2k0^4))/(8k^2k0), 0, (35(127c^8 - (504I)c^7k0 - 868c^6k0^2 + (840I)c^5k0^3 + 490c^4k0^4 - (168I)c^3k0^5 - 28c^2k0^6))/(64k^2k0), 0, ((((c - Ik0)^3(2c - Ik0)^3)/(4k^2) + ((-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2))k0^2)/2 + (3(c - Ik0)(2c - Ik0)k0^4)/(8k^2) + (3(c - Ik0)^4(2c - Ik0)(c/k - (Ik0)/k))/(8k) + (3(c - Ik0)(2c - Ik0)^4((2c)/k - (Ik0)/k))/(8k))(2c^2((c - Ik0)^5/(16(2c - Ik0)) - ((c - Ik0)^3(2c - Ik0))/16 - ((c - Ik0)(2c - Ik0)^3)/16 + (2c - Ik0)^5/(16(c - Ik0))) - (3I)c((c - Ik0)^5/(16(2c - Ik0)) - ((c - Ik0)^3(2c - Ik0))/16 - ((c - Ik0)(2c - Ik0)^3)/16 + (2c - Ik0)^5/(16(c - Ik0)))k0 + (-(c - Ik0)^5/(16(2c - Ik0)) + ((c - Ik0)^3(2c - Ik0))/16 + ((c - Ik0)(2c - Ik0)^3)/16 - (2c - Ik0)^5/(16(c - Ik0)))k0^2 + c((c - Ik0)^5/16 + ((c - Ik0)^3k0^2)/16 - ((c - Ik0)k0^4)/16 - k0^6/(16(c - Ik0))) - Ik0((c - Ik0)^5/16 + ((c - Ik0)^3k0^2)/16 - ((c - Ik0)k0^4)/16 - k0^6/(16(c - Ik0))) - 4c((2c - Ik0)^5/16 + ((2c - Ik0)^3k0^2)/16 - ((2c - Ik0)k0^4)/16 - k0^6/(16(2c - Ik0))) + (2I)k0((2c - Ik0)^5/16 + ((2c - Ik0)^3k0^2)/16 - ((2c - Ik0)k0^4)/16 - k0^6/(16(2c - Ik0)))) + (-((c - Ik0)^3(2c - Ik0))/(2k^2) - ((c - Ik0)(2c - Ik0)^3)/(2k^2) + ((c - Ik0)(2c - Ik0)k0^2)/(2k^2))(2c^2((-5(c - Ik0)^7)/(128(2c - Ik0)) + ((c - Ik0)^5(2c - Ik0))/32 + ((c - Ik0)^3(2c - Ik0)^3)/64 + ((c - Ik0)(2c - Ik0)^5)/32 - (5(2c - Ik0)^7)/(128(c - Ik0))) - (3I)c((-5(c - Ik0)^7)/(128(2c - Ik0)) + ((c - Ik0)^5(2c - Ik0))/32 + ((c - Ik0)^3(2c - Ik0)^3)/64 + ((c - Ik0)(2c - Ik0)^5)/32 - (5(2c - Ik0)^7)/(128(c - Ik0)))k0 + ((5(c - Ik0)^7)/(128(2c - Ik0)) - ((c - Ik0)^5(2c - Ik0))/32 - ((c - Ik0)^3(2c - Ik0)^3)/64 - ((c - Ik0)(2c - Ik0)^5)/32 + (5(2c - Ik0)^7)/(128(c - Ik0)))k0^2 + c((-5(c - Ik0)^7)/128 - ((c - Ik0)^5k0^2)/32 + ((c - Ik0)^3k0^4)/64 - ((c - Ik0)k0^6)/32 - (5k0^8)/(128(c - Ik0))) - Ik0((-5(c - Ik0)^7)/128 - ((c - Ik0)^5k0^2)/32 + ((c - Ik0)^3k0^4)/64 - ((c - Ik0)k0^6)/32 - (5k0^8)/(128(c - Ik0))) - 4c((-5(2c - Ik0)^7)/128 - ((2c - Ik0)^5k0^2)/32 + ((2c - Ik0)^3k0^4)/64 - ((2c - Ik0)k0^6)/32 - (5k0^8)/(128(2c - Ik0))) + (2I)k0((-5(2c - Ik0)^7)/128 - ((2c - Ik0)^5k0^2)/32 + ((2c - Ik0)^3k0^4)/64 - ((2c - Ik0)k0^6)/32 - (5k0^8)/(128(2c - Ik0)))) + ((c - Ik0)(2c - Ik0)(2c^2((7(c - Ik0)^9)/(256(2c - Ik0)) - (5(c - Ik0)^7(2c - Ik0))/256 - ((c - Ik0)^5(2c - Ik0)^3)/128 - ((c - Ik0)^3(2c - Ik0)^5)/128 - (5(c - Ik0)(2c - Ik0)^7)/256 + (7(2c - Ik0)^9)/(256(c - Ik0))) - (3I)c((7(c - Ik0)^9)/(256(2c - Ik0)) - (5(c - Ik0)^7(2c - Ik0))/256 - ((c - Ik0)^5(2c - Ik0)^3)/128 - ((c - Ik0)^3(2c - Ik0)^5)/128 - (5(c - Ik0)(2c - Ik0)^7)/256 + (7(2c - Ik0)^9)/(256(c - Ik0)))k0 + ((-7(c - Ik0)^9)/(256(2c - Ik0)) + (5(c - Ik0)^7(2c - Ik0))/256 + ((c - Ik0)^5(2c - Ik0)^3)/128 + ((c - Ik0)^3(2c - Ik0)^5)/128 + (5(c - Ik0)(2c - Ik0)^7)/256 - (7(2c - Ik0)^9)/(256(c - Ik0)))k0^2 + c((7(c - Ik0)^9)/256 + (5(c - Ik0)^7k0^2)/256 - ((c - Ik0)^5k0^4)/128 + ((c - Ik0)^3k0^6)/128 - (5(c - Ik0)k0^8)/256 - (7k0^10)/(256(c - Ik0))) - Ik0((7(c - Ik0)^9)/256 + (5(c - Ik0)^7k0^2)/256 - ((c - Ik0)^5k0^4)/128 + ((c - Ik0)^3k0^6)/128 - (5(c - Ik0)k0^8)/256 - (7k0^10)/(256(c - Ik0))) - 4c((7(2c - Ik0)^9)/256 + (5(2c - Ik0)^7k0^2)/256 - ((2c - Ik0)^5k0^4)/128 + ((2c - Ik0)^3k0^6)/128 - (5(2c - Ik0)k0^8)/256 - (7k0^10)/(256(2c - Ik0))) + (2I)k0((7(2c - Ik0)^9)/256 + (5(2c - Ik0)^7k0^2)/256 - ((2c - Ik0)^5k0^4)/128 + ((2c - Ik0)^3k0^6)/128 - (5(2c - Ik0)k0^8)/256 - (7k0^10)/(256(2c - Ik0)))))/k^2 + ((11c^4 - (24I)c^3*k0