Abstract
Since the study by Jacobi and Hecke, Hecke-type identities have received a lot of attention. In this paper, we obtain a general transformation formula for [Formula: see text]-series. Based on this formula, we derive a new [Formula: see text]-formula in this paper, which clearly includes infinitely many [Formula: see text]-identities. Other identities of Andrews and Liu and new identities for Hecke-type series are also discussed. As applications, we utilize some of these Hecke-type identities to establish families of inequalities for several partition functions.
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