Communications of the
Korean Mathematical Society CKMS

For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

Keywords: Entire function, meromorphic function, order of growth, exponent of convergence, complex differential equation

MSC numbers: Primary 34M10, 30D35