Let k be a positive integer,let h(z)■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P(f)(z)-h(z) has a...Let k be a positive integer,let h(z)■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P(f)(z)-h(z) has at most k+l-1 distinct zeros(ignoring multiplicity) in D,where P(f)(z)=f(k)(z)+a1(z)f((k-1)(z)+…+ak(z)f(z) is a differential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D,then F is normal in D.展开更多
文摘Let k be a positive integer,let h(z)■0 be a holomorphic functions in a domain D,and let F be a family of zero-free meromorphic functions in D,all of whose poles have order at least l.If,for each f∈P(f)(z)-h(z) has at most k+l-1 distinct zeros(ignoring multiplicity) in D,where P(f)(z)=f(k)(z)+a1(z)f((k-1)(z)+…+ak(z)f(z) is a differential polynomial of f and aj(z)(j=1,2,···,k) are holomorphic functions in D,then F is normal in D.
