Ramanujan theta function

Summary

Ramanujan's general theta function is $f(a, b) = \sum_{n \in \Z} a^{n(n+1)/2} b^{n(n-1)/2}$ for complex $a, b$ with $\abs{ab} < 1$. It is a two-variable form of the Jacobi theta function, symmetric in $a$ and $b$. By the Jacobi triple product it is an infinite product. Its special cases $\varphi(q)$, $\psi(q)$ and $f(-q)$ are the theta functions that Ramanujan used for partitions and modular equations.