The Ramanujan Journal

, Volume 23, Issue 1–3, pp 417–431 | Cite as

On the Andrews–Schur proof of the Rogers–Ramanujan identities



In this article, we study one of Andrews’ proofs of the Rogers–Ramanujan identities published in 1970. His proof inspires connections to some famous formulas discovered by Ramanujan. During the course of study, we discovered identities such as
$$\sum_{n\geq0}\frac{q^{n^2}}{(q;q)_n}=\frac{1}{\sqrt{5}}\Biggl(\beta \prod_{n=1}^{\infty}\frac{1}{1+\alpha q^{n/5}+q^{2n/5}}-\alpha \prod_{n=1}^{\infty}\frac{1}{1+\beta q^{n/5}+q^{2n/5}}\Biggr),$$
where β=−1/α is the Golden Ratio.


Andrews–Schur proof Rogers–Ramanujan identities 

Mathematics Subject Classification (2000)

05A15 05A30 05A40 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.University of Illinois at SpringfieldSpringfieldUSA

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