DLMF:13.15.E19 (Q4544)

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DLMF:13.15.E19
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    d n d z n ( e - 1 2 z z - μ - 1 2 M κ , μ ( z ) ) = ( - 1 ) n ( 1 2 + μ + κ ) n ( 1 + 2 μ ) n e - 1 2 z z - μ - 1 2 ( n + 1 ) M κ + 1 2 n , μ + 1 2 n ( z ) , derivative 𝑧 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 superscript 1 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 Pochhammer 1 2 𝜇 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 𝑛 1 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(e^% {-\frac{1}{2}z}z^{-\mu-\frac{1}{2}}M_{\kappa,\mu}\left(z\right)\right)=(-1)^{n% }\frac{{\left(\frac{1}{2}+\mu+\kappa\right)_{n}}}{{\left(1+2\mu\right)_{n}}}e^% {-\frac{1}{2}z}z^{-\mu-\frac{1}{2}(n+1)}\*M_{\kappa+\frac{1}{2}n,\mu+\frac{1}{% 2}n}\left(z\right),}}
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