Asymptotics of a Mathieu-Gaussian series

2021/01/04 by R. B. Paris, Paris, R B
Mathematics · #30E15 #33C15 #33E20 #34E05 #41A60 #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2101.01589

openalex publication_date 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the asymptotic expansion of the functional series S_μ,γ(a;λ)=∑_n=1^∞ \fracn^γe^-λn2/a2(n²+a²)^μ for real values of the parameters γ, λ>0 and μ≥0 as |a|→ ∞ in the sector |arg a|

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