A NOTE ON A HYPERGEOMETRIC SERIES BASED SOLUTION TO THE BASEL PROBLEM

In a very recent paper, Campbell [A Wilf-Zeilbeger based solution to the Basel problem with applications, Discrete Math. Lett. 10 (2022), 21-27], after re-writing the Basel series into a 3F2(1) hypergeometric series, pointed out that “it is not obvious as to have classically known hypergeometric identities for 3F2(1)-series with free parameters such as those of Dixon’s summation identity, Whipple’s summation identity orWatson’s summation identity could be used to determine a full proof for the closed form 3F2(1)-Basel series”. Thus the aim of this note is to provide the solution of the 3F2(1)-Basel series via the above-mentioned three summation identities.