Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 47 (2022) no. 1
Citer cet article
Gradimir V. Milovanović; Nevena M. Vasović. Some Modifications of the Chebyshev Measures and the Corresponding Orthogonal Polynomials. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 47 (2022) no. 1. http://geodesic.mathdoc.fr/item/BASS_2022_47_1_a4/
@article{BASS_2022_47_1_a4,
author = {Gradimir V. Milovanovi\'c and Nevena M. Vasovi\'c},
title = {Some {Modifications} of the {Chebyshev} {Measures} and the {Corresponding} {Orthogonal} {Polynomials}},
journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
pages = {67 - 83},
year = {2022},
volume = {47},
number = {1},
url = {http://geodesic.mathdoc.fr/item/BASS_2022_47_1_a4/}
}
TY - JOUR
AU - Gradimir V. Milovanović
AU - Nevena M. Vasović
TI - Some Modifications of the Chebyshev Measures and the Corresponding Orthogonal Polynomials
JO - Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
PY - 2022
SP - 67
EP - 83
VL - 47
IS - 1
UR - http://geodesic.mathdoc.fr/item/BASS_2022_47_1_a4/
ID - BASS_2022_47_1_a4
ER -
%0 Journal Article
%A Gradimir V. Milovanović
%A Nevena M. Vasović
%T Some Modifications of the Chebyshev Measures and the Corresponding Orthogonal Polynomials
%J Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles
%D 2022
%P 67 - 83
%V 47
%N 1
%U http://geodesic.mathdoc.fr/item/BASS_2022_47_1_a4/
%F BASS_2022_47_1_a4
A few rational modifications of the Chebyshev measures of the first and second kind and the corresponding orthogonal polynomials on the finite interval $[-1,1]$ are studied, included also a convex combination of these two Chebyshev measures. Also, an non-rational modification of the Chebyshev measure of the second kind, i.e., ${\D}\sigma ^{n,s}(x)=|\widehat U_{n}(x)|^{2s}(1-x^2)^{s+1/2}\D x$ on $[-1,1]$, for $n\in\NN$ and a real number $s>-1/2$, is studied, as well as certain properties of the corresponding orthogonal polynomials, including explicit expressions for the coefficients in their three-term recurrence relation.
