$q$-Chebyshev polynomials and their $q$-classical characters
Problemy analiza, Tome 11 (2022) no. 1, pp. 81-101.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, we give some properties of the $q$-Chebyshev polynomials through the Stieltjes function associated with their regular forms (linear functional). Some connection formulas are highlighted. The integral representation of those forms are given.
Keywords: $q$-difference equation, $H_q$-semiclassical polynomials, orthogonality measure.
@article{PA_2022_11_1_a6,
     author = {M. Mejri},
     title = {$q${-Chebyshev} polynomials and their $q$-classical characters},
     journal = {Problemy analiza},
     pages = {81--101},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_1_a6/}
}
TY  - JOUR
AU  - M. Mejri
TI  - $q$-Chebyshev polynomials and their $q$-classical characters
JO  - Problemy analiza
PY  - 2022
SP  - 81
EP  - 101
VL  - 11
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2022_11_1_a6/
LA  - en
ID  - PA_2022_11_1_a6
ER  - 
%0 Journal Article
%A M. Mejri
%T $q$-Chebyshev polynomials and their $q$-classical characters
%J Problemy analiza
%D 2022
%P 81-101
%V 11
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2022_11_1_a6/
%G en
%F PA_2022_11_1_a6
M. Mejri. $q$-Chebyshev polynomials and their $q$-classical characters. Problemy analiza, Tome 11 (2022) no. 1, pp. 81-101. http://geodesic.mathdoc.fr/item/PA_2022_11_1_a6/

[1] Atakishiyeva M., Atakishiyev N., “On discrete $q$-extension of Chebyshev polynomials”, Commun. Math. Anal., 14:2 (2013), 1–12

[2] Ben Hadj ali B., Mejri M., “Algebraic equation and symmetric second degree forms of class two”, Integral Transforms Spec. Funct., 28:9 (2017), 682–701 | DOI

[3] Chihara T. S., An introduction to orthogonal polynomials, Gordon and Breach, New york, 1978

[4] Ecran E., Cetin M., Tuglu N., “Incomplete $q$-Chebyshev polynomials”, Filomat, 32:10 (2018), 3599–3607 | DOI

[5] Gasper G, Rahman M., Basic Hypergeometric Functions, 2nd ed., Cambridge Univ. Press, 2004 | DOI

[6] Khériji L, Maroni P., “The $H_q$-classical orthogonal polynomials”, Acta. Appl. Math., 71 (2002), 49–115 | DOI

[7] Khériji L., “An introduction to the $H_q$-semiclassical”, Methods Appl. Anal., 10:3 (2003), 387–412

[8] Kizilates C, Tuğlu N, Çekim B., “On the $(p,q)$-Chebyshev polynomials and related polynomials”, Mathematics, 7(136) (2019), 1–12 | DOI

[9] Koekoek R, Lesky P. A, Swarttouw R. F., Hypergeometric Orthogonal Polynomials and Their $q$-Analoguess, Springer, 2010 | DOI

[10] Maroni P., “An introduction to second degree forms”, Adv Comput Math., 3:1–2 (1995), 59–88 | DOI

[11] Maroni P., “Une théorie algébrique des polynômes orthogonaux. Application aux polynômes orthogonaux semi-classiques”, Orthogonal Polynomials and their applications, Proc. Erice (1990), Ann. Comput. Appl. Math., 9, IMACS, 1991, 95–130

[12] Maroni P., Fonctions eulriennes. Polynmes orthogonaux classiques, A54v1, 1994, 30 pp.

[13] Maroni P., “Semi-classical character and finite-type relations between polynomial sequences”, Appl Numer Math., 31:3 (1999), 295–330 | DOI

[14] Maroni P., Mejri M., “The $I(q,\omega)$ classical orthogonal polynomials”, Appl. Numer. Math., 43:4 (2002), 423–458 | DOI

[15] Mejri M., “$q$-Extension of generalized Gegenbauer polynomials”, J. Difference Equ. Appl., 16:12 (2010), 1367–1380 | DOI

[16] Rivlin T. J., The Chebyshev Polynomials, Wiley-Interscience, New York, 1974

[17] Spencer B. G., The classical orthogonal polynomials, World Scientific Publishing CO Pte Ltd, 2016