On the Order of Growth of Solutions to Complex Non-homogeneous Linear Differential Equations

Abstract

In this paper, we study the order of growth of solutions to the nonhomogeneous linear differential equation f (k) +Ak−1e f (k−1) + · · ·+A1ef ′ +A0ef = F1e + F2e, where Aj (z) ( 6≡ 0) (j = 0, 1, · · · , k − 1), Fj (z) ( 6≡ 0) (j = 1, 2) are entire functions and a, b are complex numbers such that ab (a− b) 6= 0.