The main purpose of this paper is to show some relations between the Riemann zeta function and the generalized Bernoulli polynomials of level m. Our approach is based on the use of Fourier expansions for the periodic generalized Bernoulli functions of level m, as well as quadrature formulae of Euler-Maclaurin type. Some illustrative examples involving such relations are also given.
Classification
subjects
Mathematics
keywords
bernoulli polynomials; euler-maclaurin quadrature formulae; generalized bernoulli polynomials of level m; quadrature formula; riemann zeta function