A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is sum_(n = - ∞)^∞ (a)_n/(b)_n x^n = ((a x)_∞ (q/a x)_∞ (q)_∞ (b/a)_∞)/((x)_∞ (b/a x)_∞ (b)_∞ (q/a)_∞), where the notation (q)_k denotes q-series. For b = q, this becomes the q-binomial theorem.

Jacobi triple product | q-binomial theorem | q-series