( z d d z z ) n ( e − 1 2 z z κ − 1 M κ , μ ( z ) ) = ( 1 2 + μ + κ ) n e − 1 2 z z κ + n − 1 M κ + n , μ ( z ) \left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}\left(e^{-\frac{1}{2}z}z^{\kappa-1}M_{\kappa,\mu}\left(z\right)\right)={\left(\tfrac{1}{2}+\mu+\kappa\right)_{n}}e^{-\frac{1}{2}z}z^{\kappa+n-1}M_{\kappa+n,\mu}\left(z\right)