Closed-form evaluations of definite integrals and associated infinite series involving the Riemann zeta function

Author: Joon Cho Young  

Publisher: Taylor & Francis Ltd

ISSN: 0020-7160

Source: International Journal of Computer Mathematics, Vol.83, Iss.5-6, 2006-05, pp. : 461-472

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Abstract

A class of definite integrals are evaluated using the Cauchy residue theorem. These evaluations are then used to obtain closed-form expressions for several infinite series associated with the Riemann zeta function. A number of interesting (known or new) special cases and consequences of the main results are also considered.