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On the Proofs of the Rogers-Ramanujan Identities

  • Conference paper
q-Series and Partitions

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((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)

Partially supported by National Science Foundation Grant DMS-8702695.

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Authors and Affiliations

  1. College of Science, Department of Mathematics, The Pennsylvania State University, 215 McAllister Building, University Park, Pennsylvania, 16802, USA

    George E. Andrews

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  1. George E. Andrews
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  1. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Dennis Stanton

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Andrews, G.E. (1989). On the Proofs of the Rogers-Ramanujan Identities. In: Stanton, D. (eds) q-Series and Partitions. The IMA Volumes in Mathematics and Its Applications, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0637-5_1

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  • DOI: https://doi.org/10.1007/978-1-4684-0637-5_1

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