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Article
An Euler-type formula for ζ(2k +1)
Journal of Number Theory
(2006)
Abstract
In this short paper, we give several new formulas for ζ(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.
Keywords
- Riemann Zeta function,
- Euler’s formula,
- Euler polynomial,
- Bernoulli number.
Disciplines
Publication Date
2006
Publisher Statement
The Journal of Number Theory is published by Elsevier, http://www.journals.elsevier.com/journal-of-number-theory/.
Citation Information
Tian-Xiao He and Michael J. Dancs. "An Euler-type formula for ζ(2k +1)" Journal of Number Theory Vol. 118 Iss. 2 (2006) Available at: http://works.bepress.com/tian_xiao_he/27/