IJPAM: Volume 88, No. 1 (2013)

BERNOULLI POLYNOMIALS,
FOURIER SERIES AND ZETA NUMBERS

Ernst E. Scheufens
DTU Compute
Technical University of Denmark
DK-2800 Kgs. Lyngby, DENMARK


Abstract. Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series.

Received: June 18, 2013

AMS Subject Classification: 33, 40, 41, 42

Key Words and Phrases: Bernoulli polynomials, Fourier series, zeta numbers, integral representations, rapidly convergent series

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DOI: 10.12732/ijpam.v88i1.5 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 88
Issue: 1