DLMF:13.7.E1

MaRDI QIDQ5106

• Label: DLMF:13.7.E1

Digital Library of Mathematical Functions ID 13.7.E1

${\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,x\right)\sim\frac{e^{x}x^{a-b}}{\Gamma\left(a\right)}\sum_{s=0}^{\infty}\frac{{\left(1-a\right)_{s}}{\left(b-a\right)_{s}}}{s!}x^{-s},}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$: Olver’s confluent hypergeometric function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle\sim}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
 

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