Evaluations of some classes of the trigonometric moment integrals
Abstract
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)
WoS: 000261844900023
Scopus: 2-s2.0-56649099050
Related items
Showing items related by title, author, creator and subject.
-
Closed-form evaluations of certain definite integrals by employing the Cauchy integral theorem
Cvijović, Đurđe; Srivastava, H. M. (Numerical Algorithms, 2008) -
Integral representations of the Legendre chi function
Cvijović, Đurđe (Journal of Mathematical Analysis and Applications, 2007) -
New integral representations of the polylogarithm function
Cvijović, Đurđe (Proceedings of the Royal Society. A: Mathematical, Physical and Engineering Sciences, 2007)