Value Distribution and Arbitrary-Order Derivatives of Meromorphic Solutions of Complex Linear Differential Equations in the Unit Disc

Abstract

In this paper, we investigate the value distribution of meromorphic solutions and their arbitrary-order derivatives of the complex linear differential equation f ′ ′ + A ( z ) f ′ + B ( z ) f = F ( z ) in Δ with analytic or meromorphic coefficients of finite iterated p-order, and obtain some results on the estimates of the iterated exponent of convergence of meromorphic solutions and their arbitrary-order derivatives taking small function values.

Keywords

• complex linear differential equation
• unit disc
• meromorphic solution
• arbitrary-order derivative
• small function