DLMF:5.13.E1 (Q2158)

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Language	Label	Description	Also known as
English	DLMF:5.13.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}% \Gamma\left(s+a\right)\Gamma\left(b-s\right)z^{-s}\mathrm{d}s=\frac{\Gamma% \left(a+b\right)z^{a}}{(1+z)^{a+b}}},}}

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DLMF:5.13.E1

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{\displaystyle{\displaystyle\Re(a+b)>0}}

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{\displaystyle{\displaystyle-\Re a<c<\Re b}}

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

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Defining formula

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

C5.S2.E1.m2adec

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