Asymptotics for the Taylor coefficients of certain infinite products

2019/02/28 by Chern, Shane · 3 citations
#11P55 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1902.10839

Abstract

Let (m₁,…,m_J) and (r₁,…,r_J) be two sequences of J positive integers satisfying 1≤ r_j< m_j for all j=1,…,J. Let (δ₁,…,δ_J) be a sequence of J nonzero integers. In this paper, we study the asymptotic behavior of the Taylor coefficients of the infinite product ∏_j=1^J(∏_{k≥ 1}(1-q^r_j+m_j(k-1))(1-q^-r_j+m_jk))^δ_j.

Cited by

• Proof of a conjecture of Baruah and Sarma on sign patterns of certain infinite products
• Vanishing Coefficients of q^5n+r and q^7n+r in Certain Infinite q-series Expansions
• Some conjectures of Schlosser and Zhou on sign patterns of the coefficients of infinite products

Related

• Some conjectures of Schlosser and Zhou on sign patterns of the coefficients of infinite products
• Vanishing coefficient results in four families of infinite q-products
• On the asymptotic expansions of products related to the Wallis, Weierstrass and Wilf formulas
• Asymptotics for the Fourier coefficients of eta-quotients
• On the infinite Borwein product raised to a positive real power