The Distribution of Zeros for Differential Polynomials f~kQ[f] + P[f]

The distribution of zeros for differential polynomials fkf'+ a and fkQ[f] + P[f] has been studied in [4] and [1]. There are some difficulties in proving zeros distribution of differential polynomials because of the presence of poles. So the above results are only for entire functions. In this paper, we prove that for a transcendental meromorphic function f and two differential polynomials Q[f], P[f] of f, fkQ[f] + P[f] has infinitely many zeros outside the union of the disce which do not contain the poles of f,Q[f], P[f] and the zeros of P[f]. Where f satisfies δ(∞, f) and P are weights of Q[f] and P[f]. The result improves that of [1] and [2,4,6].