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 ().

References