\[(\kappa-\mu-\tfrac{1}{2})M_{\kappa-\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)+%
(1+2\mu)\sqrt{z}M_{\kappa,\mu}\left(z\right)-(\kappa+\mu+\tfrac{1}{2})M_{%
\kappa+\frac{1}{2},\mu+\frac{1}{2}}\left(z\right)=0,\]