Formula:5335

Digital Library of Mathematical Functions ID 13.23.E4

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \int_{0}^{\infty}e^{-zt}t^{\nu-1}\WhittakerconfhyperW{\kappa}{\mu}@{t}\diff{t}=\EulerGamma@{\tfrac{1}{2}+\mu+\nu}\EulerGamma@{\tfrac{1}{2}-\mu+\nu}\*\genhyperOlverF{2}{1}@@{\tfrac{1}{2}-\mu+\nu,\tfrac{1}{2}+\mu+\nu}{\nu-\kappa+1}{\tfrac{1}{2}-z},}

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$: Whittaker confluent hypergeometric function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{\mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}$: scaled (or Olver’s) generalized hypergeometric function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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