🌙

☰

Q-gamma function

In q-analog theory, the q {\displaystyle q} -gamma function, or basic gamma function, is a generalization of the ordinary gamma function closely related to the double gamma function. It was introduced by Jackson (1905). It is given by Γ q ( x ) = ( 1 − q ) 1 − x ∏ n = 0 ∞ 1 − q n + 1 1 − q n + x = ( 1 − q ) 1 − x ( q ; q ) ∞ ( q x ; q ) ∞ {\displaystyle…

Transformation properties, Matrix version & Overview