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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

© 1996-9 Eric W. Weisstein