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Riemann zeta function for nonnegative even integers. The Riemann zeta function for negative even integers is 0 (those are the trivial zeros of the Riemann zeta function). The Riemann zeta function for nonnegative even integers is given by (note that is the only rational number for nonnegative even integers) where are the Bernoulli numbers.
The method of solution is based on the con-struction, by the methods of Muskhelishvili [5], of canonical solutions to appro-priately posed Riemann problems [5] and yields ultimately closed-form results for the desired solution.