Abstract. Fourier series for Euler polynomials is 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: January 4, 2012

AMS Subject Classification: 33, 40, 41, 42

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

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