On the Proofs of the Rogers-Ramanujan Identities

  • George E. Andrews
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

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