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 Jackson (1905), 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.
, it essentially reduces to the infinite q-Pochhammer symbol: Define Then the following formula holds with
(Felder & Varchenko (2002)).