DLMF:13.26.E8 (Q4660): Difference between revisions

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Property / constraint
 

| y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}

|y|<|x|
Property / constraint: | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}} / rank
 
Normal rank

Revision as of 17:50, 30 December 2019

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DLMF:13.26.E8
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    Statements

    e - 1 2 y ( x + y x ) μ + 1 2 n = 0 ( 1 2 + μ - κ ) n 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 Pochhammer 1 2 𝜇 𝜅 𝑛 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{{\left(\frac{1}{2}+\mu-\kappa\right)_{n}}% }{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:13.26.E8
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    | y | < | x | 𝑦 𝑥 {\displaystyle{\displaystyle|y|<|x|}}
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