( 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)