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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 2k + 1. The Rogers-Ramanujan identities are the cases k = i = 2 and k = i + 1 = 2.
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George E. Andrews (1974) studied this question.
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