DLMF:13.26.E11 (Q4663)

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DLMF:13.26.E11
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    Statements

    Defining formula
    e 1 2 ⁢ y ⁢ ( x + y x ) μ + 1 2 ⁢ ∑ n = 0 ∞ 1 n ! ⁢ ( - y x ) n ⁢ W κ + 1 2 ⁢ n , μ + 1 2 ⁢ n ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑦 𝑥 𝜇 1 2 superscript subscript 𝑛 0 1 𝑛 superscript 𝑦 𝑥 𝑛 Whittaker-confluent-hypergeometric-W 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑥 {\displaystyle{\displaystyle e^{\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{\mu+% \frac{1}{2}}\sum_{n=0}^{\infty}\frac{1}{n!}\left(\frac{-y}{\sqrt{x}}\right)^{n% }\*W_{\kappa+\frac{1}{2}n,\mu+\frac{1}{2}n}\left(x\right),}}
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    DLMF id
    DLMF:13.26.E11
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    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
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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.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ajdec
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    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1jdec
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    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1jdec
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    Q11580
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C13.S1.XMD5.m1jdec
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