Formula:2655

Digital Library of Mathematical Functions ID 5.8.E3

${\displaystyle{\displaystyle\left|\frac{\Gamma\left(x\right)}{\Gamma\left(x+\mathrm{i}y\right)}\right|^{2}=\prod_{k=0}^{\infty}\left(1+\frac{y^{2}}{(x+k)^{2}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle x\neq 0,-1,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle y}}$: real variable
 

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