Convolution of Riemann zeta-values

Abstract

In this note we are going to generalize Prudnikov's method of using a double integral to deduce relations between the Riemann zeta-values, so as to prove intriguing relations between double zeta-values of depth 2. Prior to this, we shall deduce the most well-known relation that expresses the sum ${\sum }_{j=1}^{m-2}\zeta (j+1)\zeta (m-j)$ in terms of ${\zeta }_2(1,m)$.