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)=∞Σn=1nm[(∞Σk=n1/kp)2-1/(p-1)2n2p-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.
关键词
p级数/余项/Abel求和公式
Key words
p-series/remainder term/Abel summation formula by parts
维普
万方数据