DLMF:13.2.E2

MaRDI QIDQ4989

• Label: DLMF:13.2.E2

Digital Library of Mathematical Functions ID 13.2.E2

${\displaystyle{\displaystyle M\left(a,b,z\right)=\sum_{s=0}^{\infty}\frac{{\left(a\right)_{s}}}{{\left(b\right)_{s}}s!}z^{s}=1+\frac{a}{b}z+\frac{a(a+1)}{b(b+1)2!}z^{2}+\cdots,}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)}}$: = M ( a , b , z ) notation for the Kummer confluent hypergeometric function
• ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$:
• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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