Evaluations of some classes of the trigonometric moment integrals
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Four classes of the trigonometric moment integrals are evaluated in closed form in a simple and unified manner by making use of the contour integration in conjunction with the Cauchy integral theorem. In all cases, the closed contour of the same shape is used and it is shown that the integrals are expressible only in terms of the Hurwitz zeta function and elementary functions. A number of interesting (known or new) special cases and consequences of the main results are also considered. (c) 2008 Elsevier Inc. All rights reserved.
Keywords:
Definite integration / Contour integration / Cauchy integral theorem / Integral formulas / Cotangent integral / Tangent integral / Cosecant integral / Secant integral / Hurwitz zeta function / Riemann zeta functionSource:
Journal of Mathematical Analysis and Applications, 2009, 351, 1, 244-256Projects:
- Ministry of Science of the Republic of Serbia [144004], Natural Sciences and Engineering Research Council of Canada [OGP0007353]
DOI: 10.1016/j.jmaa.2008.10.017
ISSN: 0022-247X (print)