Elliptic gamma function

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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:


where θ is the q-theta function.

When , it essentially reduces to the infinite q-Pochhammer symbol:

Multiplication Formula[edit]


Then the following formula holds with (Felder & Varchenko (2003)).