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A generalized Euler-Maclaurin formula for the Hurwitz zeta function. (English) Zbl 1141.11041
Summary: We use an evaluation of the Mellin transform of a Fourier series in terms of some Dirichlet series in order to generalize the classical Euler-Maclaurin formula for the numerical evaluation of the Riemann zeta function.

MSC:
11M35 Hurwitz and Lerch zeta functions
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References:
[1] EDWARDS H. M.: Riemann’s Zeta Function. Pure and Applied Mathematics, Vol. 58, Academic Press, New York-London, 1974. · Zbl 0315.10035
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