GROWTH ESTIMATES FOR SOLUTIONS OF LINEAR COMPLEX DIFFERENTIAL EQUATIONS

Abstract

Two methods are used to nd growth estimates (in terms of the p-characteristic) for the analytic solutions of f (k) + Ak1(z)f (k1) + + A1(z)f 0 + A0(z)f = 0 in the disc fz 2 C: jzj < Rg, 0 < R 1. By restricting to special cases, these estimates yield known results in the complex plane without appealing to the commonly used Wiman-Valiron theory.