涉及例外函数列的正规定则

Normality on the Sequence of Omitted Functions

本文讨论了在去除不正规点的区域内涉及例外函数列的亚纯函数列的特征。主要结果如下:设{f_(n)(z)}与{a_(n)(z)}是区域D内的两个亚纯函数列。{f_(n)(z)}的零点与极点的重级均至少为k+2,{a_(n)(z)}的极点重级至少为k。a_(n)(z)χ/⇒a(z),a(z)(≠0)是D内的亚纯函数。假设f^((k))_(n)(z)≠a_(n)(z)且{f_(n)(z)}的任意子列在z_(0)∈D不正规,则在D\a^(-1)(∞)内,f^((k))_(n)(z)⇒a(z)。

The characteristic of a sequence of meromorphic functions is considered concerning the sequence of omitted functions in the domain which removes the non-normal points.The main result is as follows.Let{f_(n)(z)}and{a_(n)(z)}be two sequences of meromorphic functions in D.The zeros and poles of{f_(n)(z)}have multiplicity no less than k+2,and the poles of{a_(n)(z)}have multiplicity at least k.a_(n)(z)χ/⇒a(z),where a(z)(≠0)is meromorphic in D.Suppose that f^((k))_(n)(z)≠a_(n)(z)and any subsequence of{f_(n)(z)}is not normal at z_(0)∈D,then f^((k))_(n)(z)⇒a(z)in D\a^(-1)(∞).