ON THE VALUE DISTRIBUTION THEORY OF DIFFERENTIAL POLYNOMIALS IN THE UNIT DISC

Abstract

In this paper, we investigate the relationship between small functions and non-homogeneous differential polynomials gk = dk (z) f (k) + +d1 (z) f 0 +d0 (z) f +b(z) ; where d0 (z) ; d1 (z) ; ; dk (z) and b(z) are finite [p;q]ð€€€order meromorphic functions in the unit disc D and k 2 is an integer, which are not all equal to zero generated by the complex higher order non-homogeneous linear differential equation f (k)+Akð€€€1 (z) f (kð€€€1)+ +A1 (z) f 0 +A0 (z) f = F; for (k 2) ; where A0 (z) ; A1 (z) ; ; Akð€€€1 (z) are finite [p;q]ð€€€order meromorphic functions in unit disc D.