# Whittaker function of the first kind Calculator

## Calculates Whittaker function of the first kind Mk,m(z).

 $\normal M_{k,m}(z)=e^{-{\normal\frac{z}{2}}}z^{\small m+{\normal\frac{1}{2}}}{}_1F_1 (m-k+\frac{1}{2};2m+1;z)\\$
 k m z 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt Mk,m(z)
 $\normal Whittaker\ differential\ equation\\[10](1)\ y''+(\frac{1}{4}-\frac{k}{z}+\frac{m^2-{\normal\frac{1}{4}}}{z^2})y=0\\\hspace{25} y=c_1M_{k,m}(z)+c_2W_{k,m}(z)\\[10](2)\ M_{k,m}(z)=e^{-{\normal\frac{z}{2}}}z^{\small m+{\normal\frac{1}{2}}}{}_1F_1 (m-k+\frac{1}{2};2m+1;z)\\[10](3)\ W_{k,m}(z)=e^{-{\normal\frac{z}{2}}}z^{\small m+{\normal\frac{1}{2}}}U(m-k+\frac{1}{2}\hspace{1},2m+1,z)\\$

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