Formula:5327

Digital Library of Mathematical Functions ID 13.21.E22

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \WhittakerconfhyperM{\kappa}{\mu}@{x}=\frac{1}{2\pi}\*\EulerGamma@{2\mu+1}\*\EulerGamma@{\kappa-\mu+\tfrac{1}{2}}\*\widehat{c}(\kappa,\mu)\*\widehat{\Psi}(\kappa,\mu,x)\*\left(\sin@{\kappa\pi-\mu\pi}\AiryAi@{\kappa^{\frac{2}{3}}\widehat{\zeta}}+\cos@{\kappa\pi-\mu\pi}\AiryBi@{\kappa^{\frac{2}{3}}\widehat{\zeta}}+\envAiryBi@{\kappa^{\frac{2}{3}}\widehat{\zeta}}\bigO@{\kappa^{-1}}\right),}

Constraint(s)

Symbols List

${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$ :
${\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}$ :
${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$ : order not exceeding
${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ : gamma function
${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$ : Whittaker confluent hypergeometric function
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \cpi} : the ratio of the circumference of a circle to its diameter
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \cos@@{\NVar{z}}} : cosine function
${\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}$ :
${\displaystyle{\displaystyle\sin\NVar{z}}}$ : sine function
${\displaystyle{\displaystyle x}}$ : real variable
${\displaystyle{\displaystyle\widehat{c}(\kappa,\mu)}}$ : function (locally)
${\displaystyle{\displaystyle\widehat{\Psi}(\kappa,\mu,x)}}$ : function (locally)

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