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Zeitschrift für Analysis und ihre Anwendungen


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Volume 19, Issue 3, 2000, pp. 831–846
DOI: 10.4171/ZAA/982

Published online: 2000-09-30

Some Definite Integrals Associated with the Riemann Zeta Function

H.M. Srivastava[1], M. Lawrence Glasser[2] and V.S. Adamchik[3]

(1) University of Victoria, Victoria, Canada
(2) Clarkson University, Potsdam, USA
(3) Carnegie Mellon University, Pittsburgh, USA

The authors aim at deriving a family of series representations for $\zeta (2n + 1) (n \in \mathbb N)$ by evaluating certain trigonometric integrals in several different ways. They also show how the results presented in this paper relate to those that were obtained in other works. Finally, some illustrative computational examples, using $Mathematica$ (Version 4.0) for Linux, are considered.

Keywords: Zeta functions, trigonometric integrals, Clausen functions, series representations, trigonometric sums, Mellin transforms

Srivastava H.M., Glasser M. Lawrence, Adamchik V.S.: Some Definite Integrals Associated with the Riemann Zeta Function. Z. Anal. Anwend. 19 (2000), 831-846. doi: 10.4171/ZAA/982