On the order and the lower order of differential polynomials

Suppose that $f$ is a meromorphc function with order $\sigma(f)$ and lower order $\mu(f)$. Suppose that $P[f]$ is a differential polynomial of $f$. In this paper, it is shown that the order and the lower order of $P[f]$ are equal to the order and the lower order of $f$ under certain conditions on the degree of the differential polynomial $P[f]$, \textit{i.e.}, $\sigma(P)=\sigma(f)$ and $\mu(P)=\mu(f)$. This result improves previous results.