DLMF:13.23.E1 (Q4635): Difference between revisions

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DLMF:13.23.E1
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${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-zt}t^{\nu-1}M_{\kappa,\mu}% \left(t\right)\mathrm{d}t=\frac{\Gamma\left(\mu+\nu+\tfrac{1}{2}\right)}{\left% (z+\frac{1}{2}\right)^{\mu+\nu+\frac{1}{2}}}\*{{}_{2}F_{1}}\left({\tfrac{1}{2}% +\mu-\kappa,\tfrac{1}{2}+\mu+\nu\atop 1+2\mu};\frac{1}{z+\frac{1}{2}}\right),}}$
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DLMF:13.23.E1
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${\displaystyle{\displaystyle\Re(\mu+\nu+\tfrac{1}{2})>0}}$
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${\displaystyle{\displaystyle\Re z>\tfrac{1}{2}}}$
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${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}$
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${\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}$
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${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$
${\displaystyle{\displaystyle\mathrm{e}}}$
${\displaystyle{\displaystyle\int}}$
${\displaystyle{\displaystyle\Re}}$