p-达朗贝尔判别法及其应用  

The p-D'Alembert Method and its Application

作　　者：张玉林[1] 孟程[2] 赵茂先[1] 董晓敏[1] 葛晓晶 ZHANG Yu-lin MENG Cheng ZHAO Mao- xian DONG Xiao-min GE Xiao-jing(College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao Shandong 266590, China College of Information Science and Engineering, University of Science and Technology Qingdao Shandong 266590, China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590 [2]山东科技大学信息科学与工程学院,山东青岛266590

出　　处：《大学数学》2016年第5期71-75,共5页College Mathematics

基　　金：山东科技大学人才引进科研启动基金(2014RCJJ033);国家自然科学基金(61572128)

摘　　要：对正项级数的达朗贝尔判别法作了推广,提出并证明了p-达朗贝尔判别法,扩大了其使用范围.进一步利用数列和子列的收敛关系,证明了其与柯西判别法之间的关系.最后通过例子对p-达朗贝尔判别法进行了验证.D＇Alembert discriminance is promoted to the p-DPAlembert discrimination for positive series, and then the corresponding p-D＇Alembert discrimination is proved. Further convergence relation of sequence and its sub-sequence is used to discuss the relationship between the discrimination and Cauchy discrimination. Finally, some examples of this method are Verified.

关 键 词：正项级数 达朗贝尔判别法 柯西判别法 收敛性 

分 类 号：O174[理学—数学]