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Ramanujan’s “most beautiful identity”. (English) Zbl 1181.11071

The author nicely sketches a simple proof of the following identity of Ramanujan: If \(p(n)\) is defined so that \[ \sum_ {n\geq 0}p(n)q^n=\prod_ {n\geq 1}{{1}\over{1-q^n}}, \] then \[ \sum_ {n\geq 0}p(5n+4)q^n=5\prod_ {n\geq 1}{{(1-q^{5n})^5}\over{(1-q^n)^6}}. \]

MSC:

11P81 Elementary theory of partitions