Geodesic
Special Cases of Orthogonal Polynomials on the Semicircle and Applications in Numerical Analysis
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 44 (2019), p. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Orthogonal polynomials on the semicircle was introduced by Gautschi and Milovanović in $[$Rend. Sem. Mat. Univ. Politec. Torino, Special Issue $($July $1985)$, $179-185]$ and $[$J. Approx. Theory {\bf46} $(1986)$, $230-250]$. In this paper we give an account of this kind of orthogonality, weighted generalizations mainly oriented to Chebyshev weights of the first and second kind, as well as the corresponding applications in numerical analysis. Moreover, we also present a number of new results including those for Laurent polynomials orthogonal to a semicircle and applications to quasi-singular integrals.
Classification : 30C10, 30C15, 33C47, 65D30, 65D32
Keywords: orthogonal polynomials on the semicircle, Laurent orthogonal polynomials, recurrence relation, Gaussian quadrature rule 
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     author = {Gradimir V. Milovanovi\'c},
     title = {Special {Cases} of {Orthogonal} {Polynomials} on the {Semicircle} and {Applications} in {Numerical} {Analysis}},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {1 },
     year = {2019},
     volume = {44},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2019_44_a0/}
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Gradimir V. Milovanović. Special Cases of Orthogonal Polynomials on the Semicircle and Applications in Numerical Analysis. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 44 (2019), p. 1 . http://geodesic.mathdoc.fr/item/BASS_2019_44_a0/