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})}$ I will appreciate it a lot if a solution using method involving generating functions.


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    $\begingroup$ This are the famous Rogers-Ramanujan identities. You will find plenty information in the internet. $\endgroup$ – Johann Cigler May 3 '14 at 14:32