得到一个正规定则:设α(z)和厂分别是区域D上的解析函数与解析函数族,P(z)是次数P不低于2的多项式.如果对族厂中函数f(z)和g(z),P。f(z)和P。g(z)分担α(z)IM,并且下述条件之一成立:①对任何z0∈D,P(z)-α(z0)有至少两个不同的零点;②存在z0∈D使得P(z)-α(z0)仅有一个零点β0,同时A≠lp,其中l和k分别是f(z)-β0和α(z)-α(z0)在z0处的零点重数,α(z)不是常数.那么F在D内正规.
A normal criterion is proved in this paper. Let α(z) be an analytic function and F a family of analytic functions in a domain D, P(z) be a polynomial of degree p at least 2. Iff(z) and g(z) share α(z) IM for each pairf(z),g(z) ∈F and one of the following conditions holds: (1) P(z) -α(z) has at least two distinct zeros for any z0 ∈ D ;(2) There exists z0 ∈ D such that P(z) - α (z0 ) has only one zero β0 and suppose that the multiplicities 1 and k of zeros off (z) -rio and a(z) -a(Zo) at Zo, respectively, satisfy k #lp, possibly outside finitef(z) ∈ F,α(z) being noneonstant. Then 5c" is normal in D. Some examples are given to illustrate that the conditions in above result are necessary.