Ramanujan Psi Sum

A sum which includes both the Jacobi Triple Product and the q-Binomial Theorem as special cases. Ramanujan's sum is

$$\sum_{n=-\infty}^\infty {(a)_n\over (b)_n} x^n = {(ax)_\inf... ...a)_\infty\over (x)_\infty(b/ax)_\infty(b)_\infty(q/a)_\infty},$$

where the Notation $(q)_k$ denotes q-Series. For $b=q$, this becomes the q-Binomial Theorem.

See also Jacobi Triple Product, q-Binomial Theorem, q-Series