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. 

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