On the ϕ-Order of Growth of Solutions of Complex Linear Differential Equations near an Essential Singular Point

In this article, we will take care about an interesting topic which is the study of the ϕ-order of growth of solutions of some given linear differential equations with analytic coefficients in C-{z0}, where z0∈C represents an essential singularity. What we’ll do in this paper is a generalization of the work of Long and Zeng by introducing the concept of the ϕ–order of growth near an essential singularity.