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arXiv · 2002.09906

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

Jonas Iskander·Vanshika Jain
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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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Jonas Iskander, Vanshika Jain. 2020-02-23. Hyperbolicity of Appell Polynomials of Functions in the $δ$-Laguerre-Pólya Class. https://arxiv.org/abs/2002.09906

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