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

We present a Fourier-series based method for deriving alternative expressions for zeta(2m) and related functions such as the Dirichlet eta function, and the Bernoulli and Euler numbers. Using this method, we also present generalizations of known results for infinite sums involving the zeros of Bessel functions of the first kind.