DLMF:15.4.E23 (Q5007)

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Language	Label	Description	Also known as
English	DLMF:15.4.E23	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\lim_{z\to 1-}\frac{F\left(a,b;c;z\right)}{(1-z)^{% c-a-b}}=\frac{\Gamma\left(c\right)\Gamma\left(a+b-c\right)}{\Gamma\left(a% \right)\Gamma\left(b\right)}.}}

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DLMF:15.4.E23

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Defining formula

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

C5.S2.E1.m2acdec

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$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

{\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}

C15.S2.E1.m2avdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1udec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1qdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1edec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1bdec

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