On the conditions for a special entire function relative to the partial\n theta-function and the Euler function to belong to the Laguerre-P 'olya class

2019/12/20 by Thu Hien Nguyen, Nguyen, Thu Hien
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1912.10035

openalex publication_date 2019/12/20 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss the conditions for the function F_a(z) =\n\∑_k=0^\∞ \(z^k)/((a+1)(a²+1) \… (a^k+1)), a>1, to belong to\nthe Laguerre-P 'olya class, or to have only real zeros.\n

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