| 具有亏函数的整函数与亚纯函数的复合增长性 |
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| 引用本文： | 孙建武.具有亏函数的整函数与亚纯函数的复合增长性[J].西南师范大学学报(自然科学版),2006,31(5):47-51. |
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| 作者姓名： | 孙建武 |
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| 作者单位： | 淮阴师范学院,数学系,江苏,淮安,223001 |
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| 基金项目： | 江苏省教育厅自然科学基金资助项目(02KJD110005) . |
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| 摘 要： | 设f是超越整函数,且T(r, f) = O((logr)βexp((logr)α))(0<α<1,β>0) ,即存在两个正实数K1和K2,使得K1≤(logr)Tβe(xrp,( (fl)ogr)α)≤ K2设g1和g2是超越整函数, g2的级是ρg2(0<ρg2<∞) ,又设ai(z) (i =1,2,…,n, n≤∞)是整函数,且满足T(r, ai(z))=o( T(r, g2))及∑ni =1δ(ai(z) , g2) =1和δ(ai(z) , g2) >0.如果T(r, g1) =o( T(r, g2)) (r→∞)则T(r, f(g1)) =o( T(r, f(g2))) r→∞
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| 关 键 词： | 整函数 亚纯函数 增长性 亏函数 |
| 文章编号： | 1000-5471（2006）05-0047-05 |
| 收稿时间： | 2005-09-09 |
| 修稿时间： | 2005年9月9日 |
Growth of Composite for Entire Functions and Meromorphic Functions with Deficient Functions |
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| SUN Jian-wu.Growth of Composite for Entire Functions and Meromorphic Functions with Deficient Functions[J].Journal of Southwest China Normal University(Natural Science),2006,31(5):47-51. |
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| Authors: | SUN Jian-wu |
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| Abstract: | In this paper, the following results are obtained: Let f be a transcendental meromorphic functions withT(r, f) = O((log r)βexp(log r)a) 0 ＜ a ＜ 1, β＞ 0i. e. , there exists two positive constants K1 and K2 such that K1 ≤ T(r, f)/(log r)βexp(log r)a≤ K2; let g1 and g2 are tranfunctions which satisfying T(r, ai (z)) = o(T(r, g2 )) withn∑i=1δ(ai(z), g2) = 1 δ(ai(z), g2)＞ 0If T(r, g1) = o(T(r, g2)) (r→∞), thenT(r, f(g1)) = o(T(r, f(g2))) r→∞ |
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| Keywords: | entire function meromorphic function growth deficient function |
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