New Rapidly Convergent Series Concerning ζ(2k+1) |
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作者单位: | Department of Mathematics, Ningbo University, Zhejiang 315211, P. R. China |
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基金项目: | the National Natural Science Foundation of China,Ningbo Natural Science Foundation,Research Fund of Ningbo University |
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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.
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