Formula:2881

Digital Library of Mathematical Functions ID 5.17.E3

${\displaystyle{\displaystyle G\left(z+1\right)=(2\pi)^{z/2}\exp\left(-\tfrac{1}{2}z(z+1)-\tfrac{1}{2}\gamma z^{2}\right)\*\prod_{k=1}^{\infty}\left(\left(1+\frac{z}{k}\right)^{k}\exp\left(-z+\frac{z^{2}}{2k}\right)\right).}}$

Symbols List

• ${\displaystyle{\displaystyle G\left(\NVar{z}\right)}}$: Barnes’ G -function (or double gamma function)
• ${\displaystyle{\displaystyle\gamma}}$: Euler’s constant
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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