Formula:KLS:01.06:12

<< Formula:KLS:01.06:11

formula in Some integrals

Formula:KLS:01.07:01 >>

${\displaystyle{\displaystyle{\displaystyle\frac{1}{2\pi}\int_{0}^{\infty}\left|\frac{\Gamma\left(a+\mathrm{i}x\right)\Gamma\left(b+\mathrm{i}x\right)\Gamma\left(c+\mathrm{i}x\right)}{\Gamma\left(2\mathrm{i}x\right)}\right|^{2}\,dx=\Gamma\left(a+b\right)\Gamma\left(a+c\right)\Gamma\left(b+c\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\int}}}$ : integral : http://dlmf.nist.gov/1.4#iv
${\displaystyle{\displaystyle{\displaystyle\Gamma}}}$ : Euler's gamma function : http://dlmf.nist.gov/5.2#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i

Bibliography

Equation in Section 1.6 of KLS.

URL links

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<< Formula:KLS:01.06:11

formula in Some integrals

Formula:KLS:01.07:01 >>