Weighted integration of periodic functions on the real line

摘要

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 were obtained in an analytic form. Numerical examples are also included.