DLMF:13.26.E1 (Q4653)

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DLMF:13.26.E1
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    Statements

    Defining formula
    e - 1 2 ⁢ y ⁢ ( x x + y ) μ - 1 2 ⁢ ∑ n = 0 ∞ ( - 2 ⁢ μ ) n n ! ⁢ ( - y x ) n ⁢ M κ - 1 2 ⁢ n , μ - 1 2 ⁢ n ⁡ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑥 𝑦 𝜇 1 2 superscript subscript 𝑛 0 Pochhammer 2 𝜇 𝑛 𝑛 superscript 𝑦 𝑥 𝑛 Whittaker-confluent-hypergeometric-M 𝜅 1 2 𝑛 𝜇 1 2 𝑛 𝑥 {\displaystyle{\displaystyle e^{-\frac{1}{2}y}\left(\frac{x}{x+y}\right)^{\mu-% \frac{1}{2}}\sum_{n=0}^{\infty}\frac{{\left(-2\mu\right)_{n}}}{n!}\left(\frac{% -y}{\sqrt{x}}\right)^{n}\*M_{\kappa-\frac{1}{2}n,\mu-\frac{1}{2}n}\left(x% \right),}}
    0 references
    DLMF id
    DLMF:13.26.E1
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    constraint
    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
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    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
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    Whittaker confluent hypergeometric function
    Defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2adec
    0 references
     
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