Using Abel summation formula and Newton binomial theorem,the limit of limN→∞(N∑k=1 HmkHnk(p)/k-Hm+1NHnN(p)/m+1)is obtained,where Hn(p)=n∑k=1 1/kp,m,n are non-negative integers,p,qare positive integers,andp>1.Moreover,some k=1 kp concrete examples are given whenm,ntake special values.
harmonic numberlimitsAbel summation formulazeta function
万方数据
维普
