Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials

van Diejen, J.; Emsiz, E.

doi:10.1090/proc/14186

Quadrature rules from finite orthogonality relations for Bernstein-Szegö polynomials
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by J. F. van Diejen and E. Emsiz PDF

Proc. Amer. Math. Soc. 146 (2018), 5333-5347 Request permission

Abstract:

We glue two families of Bernstein-Szegö polynomials to construct the eigenbasis of an associated finite-dimensional Jacobi matrix. This gives rise to finite orthogonality relations for this composite eigenbasis of Bernstein-Szegö polynomials. As an application, a number of Gauss-like quadrature rules are derived for the exact integration of rational functions with prescribed poles against the Chebyshev weight functions.

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