Some hypergeometric and other evaluations of ζ(2) and allied series

摘要

Numerous interesting solutions of the problem of evaluating the Riemann ζ(2) (:=∑k=1∞k−2), which was of vital importance to Euler and the Bernoulli brothers (James and John Bernoulli), have appeared in the mathematical literature ever since Euler first solved this problem in 1736. The main object of this note is to present yet another evaluation of ζ(2) and related sums by applying the theory of hypergeometric series. Some other approaches to this problem are also indicated.