How to prove this identity? $$ \sum_{n\ge 0} \frac{x^{n^2}}{(1-x)(1-x^2)\cdots(1-x^n)} = \frac{1}{\prod_{k \ge 0}(1-x^{5k+1})(1-x^{5k+4})}$$ Maybe the method using generating functions is good.
2026-03-26 11:07:07.1774523227
How to prove this identity?(perhaps related to partition)
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This is the first of the two Rogers-Ramanujan identities.
The Wikipedia site: http://en.wikipedia.org/wiki/Rogers%E2%80%93Ramanujan_identities contains a list of references where you can find proofs.