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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1974 Oct;71(10):4082–4085. doi: 10.1073/pnas.71.10.4082

An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli

George E Andrews 1
PMCID: PMC434332  PMID: 16592187

Abstract

A (k - 1)-fold Eulerian series expansion is given for II(1 - qn)-1, where the product runs over all positive integers n that are not congruent to 0,i or - i modulo 2k + 1. The Rogers-Ramanujan identities are the cases k = i = 2 and k = i + 1 = 2.

Keywords: basic hypergeometric series, partitions, combinational identities, partition identities

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