DLMF:13.14.E9 (Q4498): Difference between revisions

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Property / constraint
 

κ - 1 2 ⁢ n - 1 2 = 0 , 1 , 2 , … 𝜅 1 2 𝑛 1 2 0 1 2 … {\displaystyle{\displaystyle\kappa-\frac{1}{2}n-\frac{1}{2}=0,1,2,\dots}}

\kappa-\frac{1}{2}n-\frac{1}{2}=0,1,2,\dots
Property / constraint: κ - 1 2 ⁢ n - 1 2 = 0 , 1 , 2 , … 𝜅 1 2 𝑛 1 2 0 1 2 … {\displaystyle{\displaystyle\kappa-\frac{1}{2}n-\frac{1}{2}=0,1,2,\dots}} / rank
 
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Revision as of 17:48, 30 December 2019

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DLMF:13.14.E9
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    Statements

    Defining formula
    W κ , ± 1 2 ⁢ n ⁡ ( z ) = ( - 1 ) κ - 1 2 ⁢ n - 1 2 ⁢ e - 1 2 ⁢ z ⁢ z 1 2 ⁢ n + 1 2 ⁢ ∑ k = 0 κ - 1 2 ⁢ n - 1 2 ( κ - 1 2 ⁢ n - 1 2 k ) ⁢ ( n + 1 + k ) κ - k - 1 2 ⁢ n - 1 2 ⁢ ( - z ) k , Whittaker-confluent-hypergeometric-W 𝜅 plus-or-minus 1 2 𝑛 𝑧 superscript 1 𝜅 1 2 𝑛 1 2 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 2 𝑛 1 2 superscript subscript 𝑘 0 𝜅 1 2 𝑛 1 2 binomial 𝜅 1 2 𝑛 1 2 𝑘 Pochhammer 𝑛 1 𝑘 𝜅 𝑘 1 2 𝑛 1 2 superscript 𝑧 𝑘 {\displaystyle{\displaystyle W_{\kappa,\pm\frac{1}{2}n}\left(z\right)=(-1)^{% \kappa-\frac{1}{2}n-\frac{1}{2}}e^{-\frac{1}{2}z}z^{\frac{1}{2}n+\frac{1}{2}}% \sum_{k=0}^{\kappa-\frac{1}{2}n-\frac{1}{2}}\genfrac{(}{)}{0.0pt}{}{\kappa-% \frac{1}{2}n-\frac{1}{2}}{k}{\left(n+1+k\right)_{\kappa-k-\frac{1}{2}n-\frac{1% }{2}}}(-z)^{k},}}
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    DLMF id
    DLMF:13.14.E9
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    constraint
    κ - 1 2 ⁢ n - 1 2 = 0 , 1 , 2 , … 𝜅 1 2 𝑛 1 2 0 1 2 … {\displaystyle{\displaystyle\kappa-\frac{1}{2}n-\frac{1}{2}=0,1,2,\dots}}
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