By Shane Chern

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}.

December 21, 2019

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Asymptotics for the Taylor coefficients of certain infinite products

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