DLMF:13.15.E21 (Q4546)

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DLMF:13.15.E21
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    d n d z n ( e 1 2 z z - μ - 1 2 W κ , μ ( z ) ) = ( - 1 ) n ( 1 2 + μ - κ ) n e 1 2 z z - μ - 1 2 ( n + 1 ) W 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-W 𝜅 𝜇 𝑧 superscript 1 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜇 1 2 𝑛 1 Whittaker-confluent-hypergeometric-W 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}}W_{\kappa,\mu}\left(z\right)\right)=(-1)^{n}% {\left(\tfrac{1}{2}+\mu-\kappa\right)_{n}}e^{\frac{1}{2}z}z^{-\mu-\frac{1}{2}(% n+1)}\*W_{\kappa-\frac{1}{2}n,\mu+\frac{1}{2}n}\left(z\right),}}
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    DLMF:13.15.E21
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