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.
- Riemann Zeta function,
- Euler’s formula,
- Euler polynomial,
- Bernoulli number.
Available at: http://works.bepress.com/tian_xiao_he/27/