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Weighted integration of periodic functions on the real line. (English) Zbl 1072.65033

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)

MSC:

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
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References:

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