New Rapidly Convergent Series Concerning ζ(2k+1)  

作　　者：Cai Lian ZHOU Yun Fei WU 

机构地区：[1]Department of Mathematics, Ningbo University, Zhejiang 315211, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2011年第3期521-527,共7页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No. 10571095);Ningbo Natural Science Foundation (Grant No. 2009A610078);Research Fund of Ningbo University (Grant No. xkl09042)

摘　　要：Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.

关 键 词：Riemann zeta function rapidly convergent series. 

分 类 号：O156.4[理学—数学]