A recursive formula for even order harmonic series

摘要

A useful recursive formula for obtaining the infinite sums of even order harmonic series Σ∞n=1 (1/n2k), k = 1, 2, …, is derived by an application of Fourier series expansion of some periodic functions. Since the formula does not contain the Bernoulli numbers, infinite sums of even order harmonic series may be calculated by the formula without the Bernoulli numbers. Infinite sums of a few even order harmonic series, which are calculated using the recursive formula, are tabulated for easy reference.