DLMF:13.23.E4 (Q4638)

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Language	Label	Description	Also known as
English	DLMF:13.23.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\nu-1}W_{\kappa,\mu}% \left(t\right)\mathrm{d}t=\Gamma\left(\tfrac{1}{2}+\mu+\nu\right)\Gamma\left(% \tfrac{1}{2}-\mu+\nu\right)\*{{}_{2}{\mathbf{F}}_{1}}\left({\tfrac{1}{2}-\mu+% \nu,\tfrac{1}{2}+\mu+\nu\atop\nu-\kappa+1};\tfrac{1}{2}-z\right),}}

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DLMF:13.23.E4

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{\displaystyle{\displaystyle\Re(\nu+\tfrac{1}{2})>|\Re\mu|}}

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{\displaystyle{\displaystyle\Re z>-\tfrac{1}{2}}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2acdec

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Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

C13.S14.E3.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1acdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2acdec

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scaled (or Olver’s) generalized hypergeometric function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}

C16.S2.E5.m2adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3acdec

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Sitelinks

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