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 in terms of .
"Convolution of Riemann zeta-values." J. Math. Soc. Japan 57 (4) 1167 - 1177, October, 2005. https://doi.org/10.2969/jmsj/1150287308