Linear Differential Equations with Analytic Coefficients Having the Same Order Near a Singular Point

In this paper, we investigate the growth of solutions of the differential equation: f (k) + Ak−1 (z) exp ak−1 (z0 − z)n f (k−1) +· · ·+ A0 (z) exp a0 (z0 − z)n f = 0, where Aj (z) are analytic functions in the closed complex plane except at z0 and a j ( j = 0, . . . , k − 1) are distinct complex numbers. Other linked cases have been studied.