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

Abstract

We have discussed the problem of finding the condition on coefficients of f ′′ + A(z)f ′ + B(z)f = 0, B(z)( ≡ 0) so that all non-trivial solutions are of infinite order. The hyper-order of these non-trivial solutions of infinite order is also found when λ(A) < ρ(A) and B(z) is a transcendental entire function satisfying some conditions.