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Asymptotics for the Taylor coefficients of certain infinite products

By Shane Chern
Let (m1,,mJ)(m_1,\ldots,m_J) and (r1,,rJ)(r_1,\ldots,r_J) be two sequences of JJ positive integers satisfying 1rj<mj1\le r_j< m_j for all j=1,,Jj=1,\ldots,J. Let (δ1,,δJ)(\delta_1,\ldots,\delta_J) be a sequence of JJ 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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