Hyperbolicity of Appell Polynomials of Functions in the δ-Laguerre-Pólya Class

2020/02/23 by Jonas Iskander, Iskander, Jonas, Vanshika Jain +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2002.09906

openalex publication_date 2020/02/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We present a method for proving that Jensen polynomials associated with functions in the δ-Laguerre-Pólya class have all real roots, and demonstrate how it can be used to construct new functions belonging to the Laguerre-Pólya class. As an application, we confirm a conjecture of Ono, which asserts that the Jensen polynomials associated with the first term of the Hardy-Ramanujan-Rademacher series formula for the partition function are always hyperbolic.

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