Quadrature formulas associated with Rogers–Szegő polynomials

This paper is concerned with the estimation of integrals of 2π2π-periodic functions with respect to the Hermite weight function by passing to the unit circle of the complex plane and considering Szegő and interpolatory-type quadrature formulas with respect now to the Rogers–Szegő weight function. Several numerical experiments are given along with estimations of the error.