DLMF:13.15.E24 (Q4549)

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DLMF:13.15.E24
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    Statements

    Defining formula
    d n d z n ⁡ ( e - 1 2 ⁢ z ⁢ z - μ - 1 2 ⁢ W κ , μ ⁡ ( z ) ) = ( - 1 ) 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 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% }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 id
    DLMF:13.15.E24
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    Symbols used
    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2ajdec
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    derivative of $$f$$ with respect to $$x$$
    Defining formula
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2aidec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
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    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1idec
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    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1wdec
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