On the Growth of Meromorphic Solutions of an Algebraic Differential Equation in a Neighborhood of a Logarithmic Singular Point

Abstract

We prove that if an analytic function f with an isolated singular point at ∞ is a solution of the differential equation P(zlnz, f, f′) = 0, where P is a polynomial in all variables, then f has finite order. We study the asymptotic properties of a meromorphic solution with logarithmic singularity.