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

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