Quasi-symmetric orthogonal polynomials on the real line: moments, quadrature rules and invariance under Christoffel modifications

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 orde...

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Bibliographic Details
Published in:Computational & applied mathematics Vol. 42; no. 3
Main Authors: Veronese, Daniel O., Silva, Jairo S., Pereira, Junior A.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.04.2023
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
41A55
Moments
Quadrature rules
QD-algorithm
42C05
Orthogonal polynomials
ISSN:2238-3603, 1807-0302
Online Access:Get full text
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Summary: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.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-023-02276-z