Formulas for Odd Zeta Values and Powers of Pi

Tue, 2011-02-22 02:24 am

Marc Chamberland and Patrick Lopatto (a Grinnell High School student) published the paper "Formulas for Odd Zeta Values and Powers of Pi" which appeared in the electronic Journal of Integer Sequences (Vol. 14, Issue 2, article 11.2.5). Values for the Riemann zeta function at odd values greater than one do not seem to have a closed form. A decade ago, the Canadian mathematician Simon Plouffe experimentally found some formulas to represent these numbers using quickly converging infinite series. This paper finds and proves such formulas for all odd values.