Weighted integration of periodic functions on the real line.
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.
scientific article; zbMATH DE number 1861077