From Fourier Series to Rapidly Convergent Series for Zeta(3)

摘要

In this note we present a method for computing values of '(s) for integers s > 2. Themethod involves Fourier series, and it succeeds in giving exact values for (s) when sis even. When s is odd the method does not give values in closed form, but we showhow it can be extended to provide series expressions for (3) (and other (s)) thatconverge much more rapidly than the series that defines the function.