On [p, q]-order of growth of solutions of complex linear differential equations near a singular point

Abstract

We investigate the $[p, q]$-order of growth of solutions of the following complex linear differential equation
$$
f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_{1}(z)f'+A_{0}(z)f=0,
$$
where $A_{j}(z)$ are analytic in $\overline{\mathbb{C}}-\{z_{0}\}$, $z_{0}\in \mathbb{C}$. Some estimations of $[p, q]$-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda.