1984•Transactions of the American Mathematical SocietyRequires access

Real Zeros of Derivatives of Meromorphic Functions and Solutions of Second Order Differential Equations

Simon Hellerstein, Li‐Chien Shen, Jack Williamson

Abstract

We classify all functions $F$ meromorphic in the plane with only real zeros and real poles which satisfy the additional conditions that $F’$ has no zeros and $F''$ only real zeros. We apply this classification, in combination with some earlier results, to the study of the reality of zeros of solutions of the equation $w'' + H(z)w = 0,H$ entire.

About this research paper

What this paper is about

Why it matters

OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Meromorphic function, Mathematics, Complex plane, Order (exchange), Entire function, Plane (geometry), Pole–zero plot, Differential equation