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Szegö quadrature formulas for certain Jacobi-type weight functions

Authors:	Leyla Daruis Pablo Gonzá lez-Vera Olav Njå stad.

Affiliation:	Department of Mathematical Analysis, La Laguna University, Tenerife, Canary Islands, Spain ; Corresponding author: Department of Mathematical Analysis, La Laguna University, 38271- La Laguna, Tenerife, Spain ; Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

Abstract:	In this paper we are concerned with the estimation of integrals on the unit circle of the form $int_0^{2pi}f(e^{itheta})omega(theta)dtheta$ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type $sum_{j=1}^nlambda_jf(x_j)$ with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions related to the Jacobi functions for the interval nodes ${x_j}_{j=1}^n$ and weights ${lambda_j}_{j=1}^n$ in Szegö quadrature formulas are explicitly deduced. Illustrative numerical examples are also given.

Keywords:	Weight functions, quadrature formulas, orthogonal polynomials, Szeg" o polynomials, error bounds

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