Growth of transcendental solutions to higher-order linear differential equations with entire coefficients

Abstract

In this article, we study the growth of transcendental solutions of certain higher order linear differential equations with entire coefficients. Under some conditions, we prove that every transcendental solution is of infinite order. We also give an estimate of its hyper-order. We improve previous results by Peng and Chen [14].

Keywords

• Linear differential equation
• transcendental entire function
• order of growth
• hyper-order