DLMF:13.26.E9 (Q4661)

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DLMF:13.26.E9
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    e - 1 2 y ( x + y x ) κ n = 0 ( 1 2 + μ - κ ) n ( 1 2 - μ - κ ) n n ! ( y x + y ) n W κ - n , μ ( x ) , superscript 𝑒 1 2 𝑦 superscript 𝑥 𝑦 𝑥 𝜅 superscript subscript 𝑛 0 Pochhammer 1 2 𝜇 𝜅 𝑛 Pochhammer 1 2 𝜇 𝜅 𝑛 𝑛 superscript 𝑦 𝑥 𝑦 𝑛 Whittaker-confluent-hypergeometric-W 𝜅 𝑛 𝜇 𝑥 {\displaystyle{\displaystyle e^{-\frac{1}{2}y}\left(\frac{x+y}{x}\right)^{% \kappa}\sum_{n=0}^{\infty}\frac{{\left(\frac{1}{2}+\mu-\kappa\right)_{n}}{% \left(\frac{1}{2}-\mu-\kappa\right)_{n}}}{n!}\*\left(\frac{y}{x+y}\right)^{n}W% _{\kappa-n,\mu}\left(x\right),}}
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