一种复级数收敛半径判定的新方法及其应用  

A New Method for Determining Convergence Radius of Complex Series and Its Application

作　　者：罗光耀[1] 张利沙[2] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆工商大学计算机学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2011年第4期376-378,共3页Journal of Chongqing Technology and Business University:Natural Science Edition

摘　　要：对形如∞∑n=0cnzφ(n)的级数的收敛域(约定收敛域为开域),作了较深入的探讨,把级数的数域扩张到复数域,对指数也作了较大的扩展,并且得出了两个定理,给出了这种复级数的比较简单的判定方法,并作了较严格的理论证明。The convergence field,which is defined as open field in this paper,of the series like ∑n=0^∞cnz^φ（n） is deeply discussed,the field of series is expanded into complex field,the exponent is also largely expanded,and two theorems are obtained.A relatively simple method for determining this kind of complex series is given and has been strictly verified.

关 键 词：函数项级数 幂级数 阿贝尔定理 收敛半径 收敛区间 

分 类 号：O15[理学—数学]