Order of growth of solutions of linear complex differential equations when the coefficients have same order

TL;DR

This paper proves that solutions of certain linear complex differential equations with coefficients of the same order are of infinite order, extending the results to higher order equations.

Contribution

It establishes that when coefficients have the same order, all non-trivial solutions are of infinite order, and extends these findings to higher order differential equations.

Findings

Solutions are of infinite order when coefficients share the same order.

Results apply to higher order differential equations.

Theorems connect coefficient order with solution growth.

Abstract

This article contains the theorems which shows that when $A(z)=h_1(z)e^{P_1(z)}$ and $B(z)=h_0(z)e^{P_0(z)}$ are of same order,then all the non-trivial solutions of equation $f"+A(z)f'+B(z)f=0$ are of infinite order. Moreover we extend these results to higher order differential equations.