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<p>Based on a classical result on partitions of an integer into a finite set of positive integers, we establish a general positivity result on coefficients of certain <i>q</i>-series which uniformly refines the positivity of truncated pentagonal number series, truncated Gauss’ identities and some special cases of truncated Jacobi triple product identity. As an application, we prove two positivity conjectures due to Merca.</p>

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A general positivity result on coefficients of certain q-series

  • 期刊论文

  • 发表日期：

    2025年10月28日

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  • Ji-Cai Liu

摘要

Based on a classical result on partitions of an integer into a finite set of positive integers, we establish a general positivity result on coefficients of certain q-series which uniformly refines the positivity of truncated pentagonal number series, truncated Gauss’ identities and some special cases of truncated Jacobi triple product identity. As an application, we prove two positivity conjectures due to Merca.