DLMF:13.26.E12 (Q4664)

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DLMF:13.26.E12
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    Statements

    test
    e 1 2 ⁢ y ⁢ ( x x + y ) κ ⁢ ∑ n = 0 ∞ 1 n ! ⁢ ( - y x + y ) n ⁢ W κ + n , μ ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑥 𝑦 𝜅 superscript subscript 𝑛 0 1 𝑛 superscript 𝑦 𝑥 𝑦 𝑛 Whittaker-confluent-hypergeometric-W 𝜅 𝑛 𝜇 𝑥 {\displaystyle{\displaystyle e^{\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{% \kappa}\sum_{n=0}^{\infty}\frac{1}{n!}\left(\frac{-y}{x+y}\right)^{n}W_{\kappa% +n,\mu}\left(x\right),}}
    0 references
    DLMF id
    DLMF:13.26.E12
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    constraint
    ℜ ⁡ ( y / x ) > - 1 2 𝑦 𝑥 1 2 {\displaystyle{\displaystyle\Re(y/x)>-\frac{1}{2}}}
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    Symbols used
    Whittaker confluent hypergeometric function
    test
    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.m2aedec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
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