On entire function $e^{p(z)}{\int }_0^z\beta (t)e^{-p(t)}dt$ with applications to Tumura--Clunie equations and complex dynamics

Yueyang Zhang

Let $p(z)$ be a nonconstant polynomial and $\beta (z)$ be a small entire function of $e^{p(z)}$ in the sense of Nevanlinna. We first describe the growth behavior of the entire function…