Second-Kind Whittaker Function
Calculate the second-kind Whittaker function Wk,m(z).
| \(\normalsize W_{k,m}(z)=e^{-{\normalsize\frac{z}{2}}}z^{\small m+{\normalsize\frac{1}{2}}}U(m-k+\frac{1}{2}\hspace{1px},2m+1,z)\\\) |
| Wk,m(z) |
| \(\normalsize Whittaker\ differential\ equation\\ (1)\ y''+(\frac{1}{4}-\frac{k}{z}+\frac{m^2-{\normalsize\frac{1}{4}}}{z^2})y=0\\ \hspace{25px} y=c_1M_{k,m}(z)+c_2W_{k,m}(z)\\ (2)\ M_{k,m}(z)=e^{-{\normalsize\frac{z}{2}}}z^{\small m+{\normalsize\frac{1}{2}}}{}_1F_1 (m-k+\frac{1}{2};2m+1;z)\\ (3)\ W_{k,m}(z)=e^{-{\normalsize\frac{z}{2}}}z^{\small m+{\normalsize\frac{1}{2}}}U(m-k+\frac{1}{2}\hspace{1px},2m+1,z)\\\) |
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