Alternative expressions for the Riemann zeta and related functions at positive even integers and infinite sums involving zeros of Bessel and spherical Bessel functions of the first kind (Q6572366)

In this article under review, the author presents several alternative expressions for the even values of the Riemann zeta function \(\zeta(2m)\), and related functions such as the even values of the Dirichlet eta function \(\eta(2m)\), the Bernoulli numbers \(B_{2m}\) and the Euler numbers \(E_{2m}\). He also presents generalizations of known results for infinite sums involving the zeros of Bessel functions of the first kind. For this purpose, the main tool is to present a Fourier-series based method for deriving the above-mentioned results.