Introduction of an Elementary Method to Express $\zeta (2n+1)$ in Terms of $\zeta (2k)$ with $k\ge 1$

Abstract

In this note we give the most elementary method (as far as we know) to express $\zeta (2n+1)$ in terms of $\{\zeta (2k)|k\ge 1\}$. The method is based on only some elementary works by Leonhard Euler, so it is very instructive to non-experts or students.

arXiv commentLatex ; 11 pages ; no figure ; typos corrected. This is our mathematical note