[Infinite Order of Growth of Solutions of Second Order Linear Differential Equations

TL;DR

This paper investigates second order linear differential equations with entire coefficients, proving that all non-trivial solutions exhibit infinite order growth under various conditions on the coefficients.

Contribution

It establishes new conditions on the coefficients A(z) and B(z) that guarantee solutions are of infinite order, extending previous growth results.

Findings

All non-trivial solutions are of infinite order under certain coefficient restrictions.

The results generalize known growth theorems for differential equations with entire coefficients.

Abstract

Considering differential equation f''+A(z)f'+B(z)f=0, where A(z) and B(z) are entire complex functions, our results revolve around proving all non-trivial solutions are of infinite order taking various restrictions on coefficients A(z) and B(z).