Szegö quadrature formulas for certain Jacobi-type weight functions

In this paper we are concerned with the estimation of integrals on the unit circle of the form ∫ 2π 0 f(eiθ)ω(θ)dθ by means of the so-called Szegö quadrature formulas, i.e., formulas of the type ∑n j=1 λjf(xj) with distinct nodes on the unit circle, exactly integrating Laurent polynomials in subspaces of dimension as high as possible. When considering certain weight functions ω(θ) related to the Jacobi functions for the interval [−1, 1], nodes {xj}j=1 and weights {λj}j=1 in Szegö quadrature formulas are explicitly deduced. Illustrative numerical examples are also given.