Formula:KLS:01.06:08

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formula in Some integrals

Formula:KLS:01.06:09 >>

${\displaystyle{\displaystyle{\displaystyle\frac{1}{2\cpi\iunit}\int_{-\iunit\infty}^{\iunit\infty}\Gamma\left(a+s\right)\Gamma\left(b-s\right)z^{-s}\,ds=\Gamma\left(a+b\right)\frac{z^{a}}{(1+z)^{a+b}}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\pi}}}$ : ratio of a circle's circumference to its diameter : http://dlmf.nist.gov/5.19.E4
${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1

Bibliography

Equation in Section 1.6 of KLS.

URL links

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<< Formula:KLS:01.06:07

formula in Some integrals

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