Elliptic hypergeometric series

Summary

An elliptic hypergeometric series is a series $\sum c_n$ in which the ratio $c_{n+1}/c_n$ is an elliptic function of $n$. In ordinary hypergeometric series the ratio is a rational function of $n$. In basic hypergeometric series it is a rational function of $q^n$, and the elliptic case is the next step. The terms are built from theta functions in place of the factors $1 - aq^k$. Setting the elliptic nome $p$ to $0$ gives back basic hypergeometric series.