Elliptic gamma function

In mathematics, the elliptic gamma function is a generalization of the q-gamma function, which is itself the q-analog of the ordinary gamma function. It is closely related to a function studied by, and can be expressed in terms of the triple [gamma function]. It is given by
It obeys several identities:
and
where θ is the q-theta function.
When, it essentially reduces to the infinite q-Pochhammer symbol:

Multiplication Formula

Define
Then the following formula holds with .