DLMF:15.2.E2 (Q4978): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.2.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}{\left(b\right)_{s}}}{\Gamma\left(c+s\right)s!}z^{s}% ,}}

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DLMF:15.2.E2

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Symbols defined

$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

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{\displaystyle{\displaystyle|z|<1}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2aadec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1aadec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5aadec

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scaled (or Olver’s) generalized hypergeometric function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}

C16.S2.E5.m2adec

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Sitelinks

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