# DLMF:13.19.E2 (Q4588): Difference between revisions

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DLMF:13.19.E2
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## Statements

${\displaystyleM_{\kappa,\mu}\left(z\right)\sim\frac{\Gamma\left% (1+2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}e^{\frac{1}{2}z}z^{-% \kappa}\*\sum_{s=0}^{\infty}\frac{{\left(\frac{1}{2}-\mu+\kappa\right)_{s}}{% \left(\frac{1}{2}+\mu+\kappa\right)_{s}}}{s!}z^{-s}+\frac{\Gamma\left(1+2\mu% \right)}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}e^{-\frac{1}{2}z\pm(\frac{1% }{2}+\mu-\kappa)\pi\mathrm{i}}z^{\kappa}\*\sum_{s=0}^{\infty}\frac{{\left(% \frac{1}{2}+\mu-\kappa\right)_{s}}{\left(\frac{1}{2}-\mu-\kappa\right)_{s}}}{s% !}(-z)^{-s},}$ 0 references
DLMF:13.19.E2
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${\displaystyle{\displaystyle-\tfrac{1}{2}\pi+\delta\leq\pm\operatorname{ph}z% \leq\tfrac{3}{2}\pi-\delta}}$ 0 references
${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ 0 references
${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$ 0 references
${\displaystyleM_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}$ 0 references
${\displaystyle{\displaystyle\sim}}$ 0 references
${\displaystyle{\displaystyle\pi}}$ 0 references
${\displaystyle{\displaystyle\mathrm{e}}}$ 0 references
${\displaystyle{\displaystyle!}}$ ${\displaystyle{\displaystyle\mathrm{i}}}$ ${\displaystyle{\displaystyle\operatorname{ph}}}$ ${\displaystyles}$ 