摘要
通过Abel分部求和公式建立p级数余项的平方相关和式的极限,给出当p>1且-1≤m≤2p-2时,S(p,m)=∞∑n=1n^(m)[(∞∑k=n 1/k^(p))^(2)-1/(p-1)^(2)n^(2p-2)]的值的表达式,特别得到当p和m为正整数时,p>m+2及2p-2-m=1时的S(p,m)的计算式子,并给出6个具体的算例.
The sums of the series relating to the square of the remainder term of p-series are obtained by the Abel summation formula by parts,where the series is S(p,m)=∞∑n=1n^(m)[(∞∑k=n 1/k^(p))^(2)-1/(p-1)^(2)n^(2p-2)],and p>1,-1≤m≤2p-2.Especially,two conclusions for easy application are implied for integers p or m,and six examples are given.
作者
雷冬霞
贺云峰
黄永忠
LEI Dongxia;HE Yunfeng;HUANG Yongzhong(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China)
出处
《大学数学》
2024年第6期63-69,共7页
College Mathematics
基金
华中科技大学教学研究专项项目(2020023)。
关键词
P级数
余项
Abel求和公式
p-series
remainder term
Abel summation formula by parts
