DLMF:15.4.E9 (Q4993)

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Language	Label	Description	Also known as
English	DLMF:15.4.E9	No description defined

Statements

Defining formula

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

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DLMF:15.4.E9

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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.m2ahdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1hdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1cdec

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