Weighted integration of periodic functions on the real line

@article{Mastroianni2002WeightedIO,
title={Weighted integration of periodic functions on the real line},
author={Giuseppe Mastroianni and Gradimir V. Milovanovic},
journal={Applied Mathematics and Computation},
year={2002},
volume={128},
pages={365-378}
}

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.