Communications of the
Korean Mathematical Society CKMS

First, we find exact values of some improper integrals involving the Bernoulli polynomials by using the Euler-Maclaurin summation formula and some known asymptotic formulas. Secondly, we prove general formulas relating certain series of the Riemann zeta function to those integrals. Finally, as special cases, we deduce some already known formulas.

Keywords: Bernoulli polynomial, Euler-Maclaurin summation formula, Riemann zeta function, Gauss measure

MSC numbers: Primary 11M06, 11B68; Secondary 33E20