Convolution of Riemann zeta-values

摘要

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 ∑_(j=1)~(m-2) ζ(j + 1)C(m - j) in terms of ζ_2(1, m).