Quasi-symmetric orthogonal polynomials on the real line: moments, quadrature rules and invariance under Christoffel modifications - Veronese, Daniel O.; Silva, Jairo S.; Pereira, Junior A. (Computational & applied mathematics, 2023)
Given a , b ∈ R , m = min { a , b } and M = max { a , b } , we consider the orthogonal polynomials associated with nontrivial positive measures ϕ for which s u p p ( ϕ ) ⊂ ( - ∞ , m ] ∪ [ M , ∞ ) and ( x - a ) d ϕ ( x ) = - ( x - b ) d ϕ ( - x + a + b ) . For this class of measures, formulas in order to compute the moments, as well as formulas for the weights and nodes in the associated Gaussian quadrature rules are provided. We also show that the QD-algorithm can be applied in order to generate new orthogonal polynomials in a simple way. Several examples are given to illustrate the results obtained.