An Euler-type formula for ζ(2k+1)

被引：9
|
作者：
Dancs, MJ [1 ]
He, TX [1 ]
机构：
[1] Illinois Wesleyan Univ, Dept Math & Comp Sci, Bloomington, IL 61702 USA
来源：
JOURNAL OF NUMBER THEORY | 2006年 / 118卷 / 02期
关键词：
Riemann zeta function; Euler's formula; Euler polynomial; Bernoulli number;
D O I：
10.1016/j.jnt.2005.09.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this short paper, we give several new formulas for zeta (n) when n is an odd positive integer. The method is based on a recent proof, due to H. Tsumura, of Euler's classical result for even n. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult. (c) 2005 Elsevier Inc. All rights reserved.
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页码：192 / 199
页数：8
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