无穷乘积的敛散性判别准则与性质研究  

Convergence Criterion and Properties of Infinite Product

作　　者：张辉 许娟 ZHANG Hui;XU Juan(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2021年第4期94-97,共4页Journal of Anqing Normal University(Natural Science Edition)

基　　金：安徽省高等学校省级质量工程项目(2020mooc271);校级质量工程项目(2019aqnujyxm57);安徽省高校自然科学重点研究项目(KJ2020A0505)。

摘　　要：无穷乘积是一类特殊乘积表达式,在数学以及相关的学科研究中经常遇到。通过细致地分析无穷乘积的结构特征,结合正项无穷级数的判别准则,给出了一些无穷乘积敛散性的判别方法并讨论了其收敛性质。研究结果揭示了无穷乘积收敛的一些本质属性,特别是,如果所有的项都小于1,则正项无穷乘积一定收敛。Infinite products is a special class of product expressions,which is often encountered in mathematics and related subjects.In this paper,we give some discrimination methods of the infinite product through analyze the structural characteristics of infinite product carefully and discusses the properties of convergence combine the discrimination criterion of the positive term infinite series.In addition,we reveal some properties of the convergence of infinite products,in particular the features that the infinite product of positive terms must converge if all the terms are less than 1.

关 键 词：无穷乘积 极限 正项级数 收敛性 

分 类 号：O177.1[理学—数学]