New findings on the periodicity of entire functions and their differential polynomials

TL;DR

This paper investigates when the periodicity of an entire function can be inferred from the periodicity of its differential polynomial, providing new conditions and generalizations to previous results.

Contribution

It introduces new conditions under which the periodicity of an entire function follows from that of its differential polynomial, extending earlier findings.

Findings

Established new sufficient conditions for periodicity transfer

Generalized previous results on entire functions and differential polynomials

Provided examples illustrating the applicability of the new conditions

Abstract

In this paper, we seek to explore under what conditions the periodicity of an entire function $ f(z) $ follows from the periodicity of a differential polynomial in $ f(z) $. We improve and generalize some earlier results and we give other new findings.