DLMF:15.4.E3 (Q4986)

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Language	Label	Description	Also known as
English	DLMF:15.4.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left(\tfrac{1}{2},1;\tfrac{3}{2};-z^{2}\right)=% z^{-1}\operatorname{arctan}z,}}

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DLMF:15.4.E3

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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.m2abdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7adec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1bdec

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