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Closed-form evaluations of certain cosecant integrals and associated series involving the Riemann zeta function

H. M. Srivastava|D. Cvijovic
장전수학회 (Jangjeon Mathematical Society)|2007.07|Advanced Studies in Contemporary Mathematics|제15권 제1호|pp. 1-12

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Abstract

A class of definite cosecant integrals are evaluated by using the methodof contour integration and the Cauchy integral 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.

참고문헌 (18)

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  18. Whittaker, "A Course of Modern Analysis An Introduction to theGeneral Theory of Infinite Processes and of Analytic Functions With an Account of thePrincipal Transcendental Functions" (1963), Cambridge University Press

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