Order and Hyper-order of Solutions of Second Order Linear Differential Equations

We show that all non-trivial solutions of complex differential equation f′′+A(z)f′+B(z)f=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f''+ A(z)f'+B(z)f = 0$$\end{document} are of infinite order if coefficients A(z) and B(z) are of special type and establish a relation between the hyper-order of these solutions and the orders of coefficients A(z) and B(z). We have also extended these results to higher order complex differential equations.