DLMF:15.8.E30 (Q5087)

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Language	Label	Description	Also known as
English	DLMF:15.8.E30	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(1-\tfrac{1}{2}z\right)^{-a}F\left({\tfrac{1}% {2}a,\tfrac{1}{2}a+\tfrac{1}{2}\atop\tfrac{1}{3}a+\tfrac{5}{6}};\left(\frac{z}% {2-z}\right)^{2}\right)=F\left({a,\tfrac{1}{3}a+\tfrac{1}{3}\atop\tfrac{2}{3}a% +\tfrac{2}{3}};z\right)=(1+z)^{-a}F\left({\tfrac{1}{2}a,\tfrac{1}{2}a+\tfrac{1% }{2}\atop\tfrac{2}{3}a+\tfrac{2}{3}};\frac{4z}{(1+z)^{2}}\right),}}

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DLMF:15.8.E30

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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.m2asdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1acdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1abdec

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