DLMF:15.4.E13 (Q4997)

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Language	Label	Description	Also known as
English	DLMF:15.4.E13	No description defined

Statements

Defining formula

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

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DLMF:15.4.E13

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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.m2aldec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1ldec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1gdec

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