Weighted integration of periodic functions on the real line

Authors:
Giuseppe Mastroianni;Gradimir V. Milovanović
Affiliations:
Dipartimento di Matematica, Universitá degli Studi della Basilicata, 85100 Potenza, Italy;Faculty of Electronic Engineering, Department of Mathematics, University of Nis, P.O. Box 73, 18000 Nis, Serbia, Yugoslavia
Venue:
Applied Mathematics and Computation - Orthogonal systems and applications
Year:
2002

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Abstract

Integration of periodic functions on the real line with an even rational weight function is considered. A transformation method of such integrals to the integrals on (-1, 1) with respect to the Szegö-Bernstein weights and a construction of the corresponding Gaussian quadrature formulas are given. The recursion coefficients in the three-term recurrence relation for the corresponding orthogonal polynomials were obtained in an analytic form. Numerical examples are also included.