DLMF:13.15.E17 (Q4542)

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DLMF:13.15.E17
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    ( 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 n - κ - 1 M κ - n , μ ( z ) , superscript 𝑧 derivative 𝑧 𝑧 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 1 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Pochhammer 1 2 𝜇 𝜅 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝑛 𝜅 1 Whittaker-confluent-hypergeometric-M 𝜅 𝑛 𝜇 𝑧 {\displaystyle{\displaystyle\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^{n-\kappa-1}M_{\kappa-n,% \mu}\left(z\right),}}
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    DLMF:13.15.E17
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