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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 523618, 12 pages
http://dx.doi.org/10.1155/2013/523618
Research Article

New Recursive Representations for the Favard Constants with Application to Multiple Singular Integrals and Summation of Series

Faculty of Mathematics and Computer Science, Paisii Hilendarski University of Plovdiv, 24 Tzar Assen Street, 4000 Plovdiv, Bulgaria

Received 11 February 2013; Accepted 22 April 2013

Academic Editor: Josip E. Pecaric

Copyright © 2013 Snezhana Georgieva Gocheva-Ilieva and Ivan Hristov Feschiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

There are obtained integral form and recurrence representations for some Fourier series and connected with them Favard constants. The method is based on preliminary integration of Fourier series which permits to establish general recursion formulas for Favard constants. This gives the opportunity for effective summation of infinite series and calculation of some classes of multiple singular integrals by the Favard constants.