On A Relation Between q-Exponential And θ-Function

2006/06/30 by Ruiming Zhang, Zhang, Ruiming
Mathematics · #33D45 #33E05 #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical and Theoretical Analysis #math.CA #math.CV #msc:33D45 #msc:33E05

paper · pdf · doi:10.48550/arxiv.math/0606781

arxiv created 2006/06/30 · openalex publication_date 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We will use a discrete analogue of the classical Laplace method to show that for infinitely many positive integers n, the main term of the asymptotic expansion of the scaled q-exponential (-q^-nt+1/2u;q)_∞ could be expressed in θ-function.

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