Formula:5254

Digital Library of Mathematical Functions ID 13.16.E6

${\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{-\frac{1}{2}z}z^{\kappa+1}}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}\*\int_{0}^{\infty}\frac{W_{-\kappa,\mu}\left(t\right)e^{-\frac{1}{2}t}t^{-\kappa-1}}{t+z}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}{z}|<\pi}}$
${\displaystyle{\displaystyle\Re(\frac{1}{2}+\mu-\kappa)>\max\left(2\Re\mu,0\right)}}$

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
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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