Generalized Lambert Series Identities

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RANK DIFFERENCES FOR OVERPARTITIONS (2007, background): “Chan, is to observe that it is essentially the case r = 1, s = 3, a1 = z, b1 = z= , b2 = z , and b3 = z of [ 8, Theorem 2.1 ],”
Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols (2008, unknown): “1 of [13], we obtain S2 ( xζ, ζ; q ) + ζ(2)S2 (xζ, ζ; q)+2 J ( ζ2; q2 ) (−q; q)(2)∞ J (−ζ; q)J (ζ−1; q2)2 (x, 1; q) = J(−x; q)J ( ζ2; q2 )”
Integer Matrix Exact Covering Systems and Product Identities for Theta Functions (2010, background): “Recently, various representations of (q; q)(10) ∞ have been given in [5], [27],[13], [8],[10], and [15].”