\[\frac{2\pi}{\Gamma\left(1+2\mu\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)%
}M_{-\kappa,\mu}\left(z\right)={\mathrm{e}}^{\mu\pi\mathrm{i}}W_{\kappa,\mu}%
\left({\mathrm{e}}^{\pi\mathrm{i}}z\right)+{\mathrm{e}}^{-\mu\pi\mathrm{i}}W_{%
\kappa,\mu}\left({\mathrm{e}}^{-\pi\mathrm{i}}z\right),\]