Formula:5333

Digital Library of Mathematical Functions ID 13.23.E2

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

Constraint(s)

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

Symbols List

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \EulerGamma@{\NVar{z}}} : 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 \diff{\NVar{x}}} : differential of x
• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \expe} : base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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