How to prove this identity? $ \sum_{n\ge 0} \frac{x^{n^2}}{(1x)(1x^2)\cdots(1x^n)}= \frac{1}{\prod_{k \ge 0}(1x^{5k+1})(1x^{5k+4})}$ I will appreciate it a lot if a solution using method involving generating functions.
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8$\begingroup$ This are the famous RogersRamanujan identities. You will find plenty information in the internet. $\endgroup$ – Johann Cigler May 3 '14 at 14:32