Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coefficients are entire functions

Abstract

We investigate the growth of solutions of the differential equation f (n)+ An− 1 (z) f (n− 1)+...+ A1 (z) f+ A0 (z) f= 0, where A0 (z),..., An− 1 (z) are entire functions with A0 (z)≡ 0. We estimate the hyper-order with respect to the conditions of A0 (z),..., An− 1 (z) if f≡ 0 has infinite order.