Integral representations of the generating function of the Riemann zeta function of integer arguments

Abstract

In this article we give new integral representations for the ordinary generating functions of ζ(2n), nζ(2n+1) and ζ(2n+1) for n∈ Z*, n≥1; where  ζ(j) is the Riemann zeta function. We also give closed form expressions
for the generating functions.