广义调和级数及其推广应用研究  

General Harmonic Series and Its Application in Infinite Series

作　　者：张海燕[1] 甘犬财[1] 许新琨[1] 

机构地区：[1]解放军电子工程学院数学教研室,合肥230037

出　　处：《大学数学》2014年第6期98-104,共7页College Mathematics

摘　　要：创建了广义调和级数和广义欧拉常数函数的概念,得到了广义调和级数和广义欧拉常数一系列十分重要的性质,得到了完全和公式,近似夹公式,讨论了广义欧拉常数与黎曼和的关系.利用复数的知识,找到了一种研究级数∑n=1∞b0+b1n+…+brnr/a0+a1n+…+aknk敛散性和求和的全新思路和方法—广义调和级数法.The paper define the general harmonic series and general Euler constant, study a series of importantproperties of the general harmonic and general Euler constant, get Complete summation and approximate formula, studygeneral Euler constant and Riemann sum theorems, use plural theorems, obtain a novel method at exploring theconvergence and summation for a kind of series, the method is general harmonic series.

关 键 词：广义调和级数 欧拉常数 收敛 求和 

分 类 号：O173[理学—数学]