Growth of Solutions to Complex Linear Differential Equations with Analytic or Meromorphic Coefficients in ℂ̅ − {z0} of Finite Logarithmic Order

In this paper, by using Nevanlinna theory near a singular point, we study the growth and the oscillation of solutions of homogeneous and non-homogeneous complex linear differential equations of the form:where () ( = 0, 1, … , -1) and () are analytic or meromorphic functions in the extended complex plane except a finite singular point with finite logarithmic order.Under some additional conditions when an arbitrary () dominating near a singular point 0 ∈ ℂ the others coefficients by its logarithmic order and logarithmic type, we obtained some growth properties of solutions of the above equations.The results established in the present paper extend and improve those from other works.