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 $f^{\prime \prime }+A(z)f^{\prime }+B(z)f=0,B(z)(\not\equiv 0)$ 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.

26 pages, comments are welcome