DLMF:15.4.E29 (Q5013)

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Language	Label	Description	Also known as
English	DLMF:15.4.E29	No description defined

Statements

Defining formula

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

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DLMF:15.4.E29

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Defining formula

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

C5.S2.E1.m2agdec

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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.m2aaadec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2abdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1vdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1jdec

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Sitelinks

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