DLMF:15.4.E11 (Q4995)

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Language	Label	Description	Also known as
English	DLMF:15.4.E11	No description defined

Statements

Defining formula

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

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DLMF:15.4.E11

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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.m2ajdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1jdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1edec

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