An Euler-type formula for ζ(2k +1)

Authors

Tian-Xiao He, Illinois Wesleyan UniversityFollow
Michael Dancs

Publication Date

January 2006

Comments

The Journal of Number Theory is published by Elsevier, http://www.journals.elsevier.com/journal-of-number-theory/.

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.

Disciplines

Applied Mathematics | Mathematics

Recommended Citation

He, Tian-Xiao and Dancs, Michael, "An Euler-type formula for ζ(2k +1)" (2006). Scholarship. 5.
https://digitalcommons.iwu.edu/math_scholarship/5