Elliptic gamma function

Summary

The elliptic gamma function $\Gamma(z; p, q)$ is a two-parameter generalisation of the q-gamma function. It is a double infinite product, and shifting $z$ to $qz$ multiplies it by a theta function in the base $p$. In this way it stands to theta functions as the gamma function stands to linear functions. It is the basic object of elliptic hypergeometric series and integrals.