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

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.