包含广义调和数的级数之和  

Sums of Series Containing Generalized Harmonic Numbers

作　　者：黄永忠[1] 雷冬霞[1] HUANG Yongzhong;LEI Dongxia(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074

出　　处：《大学数学》2024年第3期62-69,共8页College Mathematics

基　　金：高等学校大学数学教学研究与发展中心2023年项目(CMC20230108)。

摘　　要：利用p级数的解析延拓,给出相应于广义调和数与zeta函数之差的几个级数的和,并给出几个应用例子;对包含收敛p级数余项的一个级数,给出其和的计算式子.For several series associated with the difference between(generalized)harmonic number and zeta function,the sums of the series are obtained by the analytic continuation of p-series,and several examples are given.Moreover,a calculation formula for the sum of the series containing the tail of the convergent p-series is obtained.

关 键 词：广义调和数 级数的和 ZETA函数 P级数 

分 类 号：O177.5[理学—数学]