在正整数变元上推广Dirichlet lambda和Riemannζ函数的两个级数

IF 1 Q1 MATHEMATICS
Lubomir Markov
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引用次数: 0

摘要

考虑级数(cid:80)∞k=0 G N(k)(2k+1)r和(cid:80%)∞k=1 H N(k。对于3≤r∈N,导出了这些级数在ζ值方面的表示,扩展了[J.Ewell,Canad.Math.Bull.34(1991)60–66]中证明的定理。得到了几个推论(特别是对于r=3的情况),扩展了一些已知的表示,包括欧拉著名的ζ(3)的快速收敛级数。该技术可应用于r=2的情况,并得到公式(cid:80)∞k=0 1(2k+1)的推广
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Two series which generalize Dirichlet’s lambda and Riemann’s zeta functions at positive integer arguments
The series (cid:80) ∞ k =0 G N ( k ) (2 k +1) r and (cid:80) ∞ k =1 H N ( k ) k r are considered, where G N ( k ) and H N ( k ) are the Borwein-Chamberland sums appeared in the expansions of integer powers of the arcsine reported in the paper [D. Borwein, M. Chamberland, Int. J. Math. Math. Sci. 2007 (2007) #1981]. For 3 ≤ r ∈ N , representations for these series in terms of zeta values are derived, extending a theorem proved in the paper [J. Ewell, Canad. Math. Bull. 34 (1991) 60–66]. Several corollaries (especially for the case r = 3 ) are obtained, extending some known representations, including Euler’s famous rapidly converging series for ζ (3) . The technique can be applied to the case r = 2 and it yields generalizations of the formulas (cid:80) ∞ k =0 1 (2 k +1
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来源期刊
Discrete Mathematics Letters
Discrete Mathematics Letters Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.50
自引率
12.50%
发文量
47
审稿时长
12 weeks
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