# On the Proofs of the Rogers-Ramanujan Identities

• George E. Andrews
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 18)

## Abstract

The celebrated Rogers-Ramanujan identities are familiar in two forms [52; pp. 33-48]. First as series-product identities:
$$1 + \sum\limits_{n = 1}^\infty {\frac{{{q^{{n^2}}}}}{{\left( {1 - q} \right)\left( {1 - {q^2}} \right) \ldots \left( {1 - {q^n}} \right)}} = \prod\limits_{n = 0}^\infty {\frac{1}{{\left( {1 - {q^{5n + 1}}} \right)\left( {1 - {q^{5n + 4}}} \right)}}} }$$
(1.1)
$$1 + \sum\limits_{n = 1}^\infty {\frac{{{q^{{n^2} + n}}}}{{\left( {1 - q} \right)\left( {1 - {q^2}} \right) \ldots \left( {1 - {q^n}} \right)}} = \prod\limits_{n = 0}^\infty {\frac{1}{{\left( {1 - {q^{5n + 2}}} \right)\left( {1 - {q^{5n + 3}}} \right)}}} }$$
(1.2)

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## Copyright information

© Springer-Verlag New York Inc. 1989

## Authors and Affiliations

• George E. Andrews
• 1
1. 1.College of Science, Department of MathematicsThe Pennsylvania State UniversityUniversity ParkUSA