Differential polynomials generated by some complex linear differential equations with meromorphic coefficients

Abstract

In this paper, we investigate the relationship between small functions and differential polynomials g (z) = d2f′′ + d1f′ + d0f, where d0 (z) , d1 (z) , d2 (z) are meromorphic functions which are not all equal to zero with ρ (dj ) < n (j = 0, 1, 2) generated by some second order linear differential equations with meromorphic coefficients.