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

Abstract

We show that all non-trivial solutions of complex differential equation $$f''+ A(z)f'+B(z)f = 0$$ 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.