Derivatives of meromorphic functions of finite order

TL;DR

This paper investigates the relationship between the zeros of the first and second derivatives of meromorphic functions of finite order, establishing a new result about their zero distribution.

Contribution

It proves a novel result linking the zeros of the derivatives of meromorphic functions of finite order, expanding understanding of their zero structure.

Findings

Zeros of the second derivative mostly coincide with zeros of the first derivative.

Provides conditions under which the zeros of derivatives are related.

Advances the theory of meromorphic functions of finite order.

Abstract

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.