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 $f''+A(z)f'+B(z)f=0, \quad B(z)(\not \equiv 0)$ 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 $\lambda(A)<\rho(A)$ and $B(z)$ is a transcendental entire function satisfying some conditions.