On the theorem of tumura-clunie

There exist many results generalizing the Theorem of Tumura–Clunie. Concerning a wider class of differential polynomials we will give a new estimate of the characteristic of f which allows to derive or improve results of Tumura/Clunie, Hayman, Mues, Steinmetz, Toda, Weissenborn, Xin-Hou Hua, Ishizaki and Yi. In this paper we examine functions of the form where f is meromorphic and transcendental p[f]. Q[f] are non-vanishing differential polynomials in f, and Q[f] is of degree γ Q < n-1 and weight г Q 1. if γ Q ≤ n 2 then: 2. if γ Q = n-1 then: