DLMF:15.8.E28 (Q5085)

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Language	Label	Description	Also known as
English	DLMF:15.8.E28	No description defined

Statements

Defining formula

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

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DLMF:15.8.E28

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}

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{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2aldec

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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.m2aqdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2ardec

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Sitelinks

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