Sign regularity of Maclaurin coefficients of functions in the Laguerre-P\'olya class

TL;DR

This paper demonstrates that for a broad class of entire functions in the Laguerre-Pólya class, the signs of their Maclaurin coefficients follow a predictable and regular pattern.

Contribution

It establishes a general result on the sign regularity of Maclaurin coefficients for functions in the Laguerre-Pólya class, extending previous understanding.

Findings

Signs of Maclaurin coefficients exhibit regular behavior.

Applicable to a wide class of entire functions in the Laguerre-Pólya class.

Provides new insights into the coefficient structure of these functions.

Abstract

We prove that the signs of the Maclaurin coefficients of a wide class of entire functions that belong to the Laguerre-P\'olya class posses a regular behaviour.