\[M_{\kappa,\mu}\left(z\right)M_{\kappa,-\mu-1}\left(z\right)+\frac{(\frac{1}{2}%
+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}M_{\kappa,\mu+1}%
\left(z\right)M_{\kappa,-\mu}\left(z\right)=1.\]