利用Gamma函数判定一类阶乘型级数的敛散性  

On Gamma Function and Positive Series with Factorial Terms

作　　者：吴慧卓 齐雪林[1] WU Huizhuo;QI Xuelin(School of Mathematics and Statistics, Xi＇an JiaotongUniversity, Xi＇an,710049, PRC)

机构地区：[1]西安交通大学数学与统计学院,陕西西安710049

出　　处：《高等数学研究》2018年第3期19-20,14,共3页Studies in College Mathematics

摘　　要：利用Gamma函数的等价定义,证明了Gamma函数极限定义中的函数序列的收敛性.通过举例说明对通项中含有"阶乘类型"的正项级数,当比值审敛法失效时,可利用Gamma函数的等价定义判定其敛散性.In this paper,an equivalent definition of Gamma function is presented and its convergence is proved.Furthermore,the equivalent definition can be used to test on three special series with the ＇factorial-type＇ if the ratio test is inapplicable.

关 键 词：GAMMA函数 正项级数 比值审敛法 

分 类 号：O13[理学—数学]