级数的常规可和,Cesàro可和与Abel可和的几点讨论  

Some notes on series standard summability, Cesàro summability and Abel summability

作　　者：张立柱[1] 

机构地区：[1]上海财经大学应用数学系,上海200433

出　　处：《纯粹数学与应用数学》2013年第6期565-571,共7页Pure and Applied Mathematics

基　　金：国家自然科学基金(11201284)

摘　　要：讨论级数常规可和、Cesàro可和与Abel可和的关系.利用数学分析级数理论,证明Abel可和适用范围最广,Cesàro可和其次,级数常规可和适用范围最小.这个结论丰富了经典级数理论,为实际应用中选用合适可和提供依据.The relationship among series standard summability, Cesaro summability and Abel summability is studied in this paper. By using series theory in mathematical analysis, it is proved that Abel summability is the strongest, and Cesaro summability is stronger than the standard summability. The conclusion enriches the classic series theory, and provides theory basis for choosing suitable summability in practical applications.

关 键 词：级数常规可和 Cesaro可和 Abel可和 

分 类 号：O173.1[理学—数学]