Infinite-Order Meromorphic Functions with Maximal Sum of Quasi-Deficiencies

The paper discusses the problem of the sum of deficiencies of meromorphic functions with maximal sum of quasi-deficiencies and improves the meromorphic function of finite to infinite,which improves the results of Niu Yingxuan and He Li.We get two conclusions of meromorphic functions with maximal sum of quasi-deficiencies.Theorem 1 Let f be a meromorphic function of infinite order,if there exists a positive integer l such that ■Θ(a,f)=2(l+1)/l-Θl)(∞,f),then ■δ(a,f)=0.Theorem 2 Let f be a meromorphic function of infinite order,if there exists a positive integer l such that ■Θl)(a,f)=l+1/l(2-Θ(∞,f)),then ■δ(a,f)=0.