Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

Abstract

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomials $L\left(f\right)=d_{2}f″+d_1{f}^{\prime }+d_{0}f$ generated by solutions of the above equation, where $d_0\left(z\right),d_1\left(z\right),$ and $d_2\left(z\right)$ are entire functions that are not all equal to zero.