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Ramanujan Psi Sum

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A Ramanujan Psi sum is 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)/((b)_n)x^n=((ax)_infty(q/ax)_infty(q)_infty(b/a)_infty)/((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

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Cite this as:

Weisstein, Eric W. "Ramanujan Psi Sum." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RamanujanPsiSum.html

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