涉及高阶导数的分担函数与正规族  

Sharing functions and normal families involving higher-order derivatives

作　　者：王皓然 杨祺[1] WANG Haoran;YANG Qi(Xingjiang Normal University,School of Mathematical Sciences,Urumqi 830017,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《商丘师范学院学报》2024年第12期1-5,共5页Journal of Shangqiu Normal University

基　　金：国家自然科学基金项目(11961068)。

摘　　要：设F是定义在复平面D上的一族亚纯函数,m≥0, n≥2, k≥1为3个正整数.设φ(z)为区域D上零点重数最少为m的解析函数,且φ(z)≢0.设P是一个多项式,deg(P)≥3,且至少有一个q重零点,m可被n+q整除.若对任意的f∈F, f的零点重数最少是k+m/q,并且极点重数最少是m+1.则对每一组(f,g)∈F,若P(f)(f^((k)))^(n)与P(g)(g^(k))^(n)分担φ(z),则F在D上正规.Take positives integers m≥0,n≥2,k≥1.Let F be a family of meromorphic functions defined in a domain D.Letφ(z)≢0 be an analytic function with zeros of multiplicity m in a domain D.Let P be a polynomial with deg(P)≥3 and had at least one q-fold zero,m can be divisible by n+q.For every f∈F,f has only zeros with multiplicity at least k+m/q,and all its poles of multiplicity at least m+1.If P(f)(f^((k)))^(n) and P(g)(g^((k)))^(n) shareφ(z)in D for each pair of(f,g)∈F,then F is normal in D.

关 键 词：正规族 分担函数 亚纯函数 

分 类 号：O174.52[理学—数学]