Elliptic Gamma Function

The elliptic gamma function is the elliptic generalization of the standard gamma function. It is defined as:

\[ \Gamma(z; p, q) = \prod_{i,j = 1}^{\infty} \frac{1 - \frac{1}{z} p^{i+1} q^{j+1}}{1 - z p^i q^j} \]

The elliptic gamma function has especial use in the context of the superconformal index, where it is the form of the superconformal index of the chiral multiplet.