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arXiv · 1902.10839

Asymptotics for the Taylor coefficients of certain infinite products

Shane Chern
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Abstract

Let $(m_1,\ldots,m_J)$ and $(r_1,\ldots,r_J)$ be two sequences of $J$ positive integers satisfying $1\le r_j< m_j$ for all $j=1,\ldots,J$. Let $(\delta_1,\ldots,\delta_J)$ be a sequence of $J$ nonzero integers. In this paper, we study the asymptotic behavior of the Taylor coefficients of the infinite product $$\prod_{j=1}^J\Bigg(\prod_{k\ge 1}\big(1-q^{r_j+m_j(k-1)}\big)\big(1-q^{-r_j+m_jk}\big)\Bigg)^{\delta_j}.$$

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Shane Chern. 2019-02-28. Asymptotics for the Taylor coefficients of certain infinite products. https://arxiv.org/abs/1902.10839

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