DLMF:15.4.E27 (Q5011)

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Language	Label	Description	Also known as
English	DLMF:15.4.E27	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left(1,a;a+1;-1\right)=\tfrac{1}{2}a\left(\psi% \left(\tfrac{1}{2}a+\tfrac{1}{2}\right)-\psi\left(\tfrac{1}{2}a\right)\right).}}

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DLMF:15.4.E27

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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.m2aydec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1tdec

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Sitelinks

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