In this work we first analyse the computation of nodes and weights for the quadrature formulas of Szegã-Lobatto associated with rational modifications of the Lebesgue measure and Rogers-Szegã measure, by using the method recently proposed by C. Jagels and L. Reichel in [1]. Secondly, we deduce the maximal domain of validity on the set of Laurent polynomials, when dealing with certain quadrature formula on the unit circle with prescribed nodes. Numerical examples concerning both quadrature formulas are carried out.

[1] C. Jagels, and L. Reichel, Szegã-Lobatto quadrature rules, J. Comp. Appl. Math. 200 (2007), 116-126.