DLMF:13.16.E9 (Q4560): Difference between revisions

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Property / constraint
 

| ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}

|\phase{z}|<\frac{1}{2}\pi
Property / constraint: | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}} / rank
 
Normal rank

Revision as of 17:49, 30 December 2019

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DLMF:13.16.E9
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    Statements

    Defining formula
    W κ , μ ⁡ ( z ) = e - 1 2 ⁢ z ⁢ z κ + c ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t c - 1 ⁢ 𝐅 1 2 ⁡ ( 1 2 + μ - κ , 1 2 - μ - κ c ; - t ) ⁢ d t , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 𝑐 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 𝑐 1 hypergeometric-bold-pFq 2 1 1 2 𝜇 𝜅 1 2 𝜇 𝜅 𝑐 𝑡 𝑡 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=e^{-\frac{1}{2}z}z^{% \kappa+c}\*\int_{0}^{\infty}e^{-zt}t^{c-1}{{}_{2}{\mathbf{F}}_{1}}\left({% \tfrac{1}{2}+\mu-\kappa,\tfrac{1}{2}-\mu-\kappa\atop c};-t\right)\mathrm{d}t,}}
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    DLMF id
    DLMF:13.16.E9
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    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\frac{1}{2}\pi}}
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