Mastroianni, Giuseppe; Milovanović, Gradimir V. Weighted integration of periodic functions on the real line. (English) Zbl 1072.65033 Appl. Math. Comput. 128, No. 2-3, 365-378 (2002). 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 Szegő-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 are obtained in an analytic form. Numerical examples are also included. Reviewer: Feng Qi (Jiaozu) Cited in 1 ReviewCited in 7 Documents MSC: 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures Keywords:Gauss type quadratures; error term; convergence; orthogonal polynomials; nonnegative measure; weights; Chebyshev weight; Szegő-Bernstein weights; nodes; modified moments; Chebyshev polynomials; periodic functions; three-term recurrence relation; numerical examples PDFBibTeX XMLCite \textit{G. Mastroianni} and \textit{G. V. Milovanović}, Appl. Math. Comput. 128, No. 2--3, 365--378 (2002; Zbl 1072.65033) Full Text: DOI References: [1] Fischer, B.; Golub, G., How to generate unknown orthogonal polynomials out of known orthogonal polynomials, J. Comput. Appl. Math., 43, 99-115 (1992) · Zbl 0764.65009 [3] Gautschi, W., Orthogonal polynomials: applications and computation, Acta Numerica, 45-119 (1996) · Zbl 0871.65011 [4] Golub, G.; Welsch, J. H., Calculation of Gauss quadrature rules, Math. Comp., 44, 221-230 (1969) · Zbl 0179.21901 [5] Mastroianni, G., Generalized Christoffel functions and error of positive quadrature, Numer. Algorithms, 10, 113-126 (1995) · Zbl 0843.41006 [6] Prudnikov, A. P.; Brychkov, Yu. A.; Marichev, O. I., Integrals and Series. Elementary Functions (1981), Nauka: Nauka Moscow, (in Russian) · Zbl 0511.00044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.