On the hyper-order of solutions of nonhomogeneous linear dierential equations

Abstract

In this paper, we study the hyper-order of solutions of   higher order linear differential equation

\begin{equation*} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\ldots A_{1}(z)f^{\prime }+A_{0}(z)f=H(z),\end{equation*}

where $k\geq 2$ is an integer, $A_{j}\left( z\right) $ $(j=0,1,\ldots,k-1)$ and $H\left( z\right) $ $\left( \not\equiv 0\right) $ are entire functions or polynomials. We improve previous results given by Xu and Cao.