Multiple gamma function

In mathematics, the multiple gamma function ${\displaystyle \Gamma _{N}}$ is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was studied by Barnes (1901). At the end of this paper he mentioned the existence of multiple gamma functions generalizing it, and studied these further in Barnes (1904).

Double gamma functions ${\displaystyle \Gamma _{2}}$ are closely related to the q-gamma function, and triple gamma functions ${\displaystyle \Gamma _{3}}$ are related to the elliptic gamma function.