Voir la notice de l'article provenant de la source Math-Net.Ru
@article{EMJ_2013_4_2_a5, author = {L. Kh\'eriji and P. Maroni}, title = {On the natural $q$-analogues of the classical orthogonal polynomials}, journal = {Eurasian mathematical journal}, pages = {82--103}, publisher = {mathdoc}, volume = {4}, number = {2}, year = {2013}, language = {en}, url = {http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a5/} }
L. Khériji; P. Maroni. On the natural $q$-analogues of the classical orthogonal polynomials. Eurasian mathematical journal, Tome 4 (2013) no. 2, pp. 82-103. http://geodesic.mathdoc.fr/item/EMJ_2013_4_2_a5/
[1] F. Abdelkarim, P. Maroni, “The $D_\omega$-classical orthogonal polynomials”, Results in Math., 32 (1997), 1–28 | DOI | MR | Zbl
[2] C. Berg, M. E. H. Ismail, “$q$-Hermite polynomials and classical orthogonal polynomials”, Canad. J. Math., 48:1 (1996), 43–63 | DOI | MR | Zbl
[3] C. Berg, A. Ruffing, “Generalized $q$-Hermite polynomials”, Commun. Math. Phy., 223:1 (2004), 29–46 | DOI | MR
[4] G. Gasper, M. Rahman, Basic hypergeometric series, Cambridge University Press, Cambridge, 1990 | MR | Zbl
[5] A. Ghressi, L. Khériji, “The symmetrical $H_q$-semiclassical orthogonal polynomials of class one”, SIGMA, 5 (2009), 076, 22 pp. | MR | Zbl
[6] F. H. Jackson, “On a $q$-definite integrals”, Quarterly J. Pure Appl. Math., 41 (1910), 193–203 | Zbl
[7] V. G. Kac, P. Cheung, Quantum calculus, Universitext, Springer-Verlag, New York, 2002 | DOI | MR
[8] O. F. Kamech, M. Mejri, “Some discrete representations of $q$-classical linear forms”, Appl. Math. E-notes, 9 (2009), 34–39 | MR | Zbl
[9] L. Khériji, P. Maroni, “The $H_q$-classical orthogonal polynomials”, Acta. Appl. Math., 71:1 (2002), 49–115 | DOI | MR | Zbl
[10] R. Koekoek, R. F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its $q$-analogue, Reports of the Faculty of Technical Mathematics and Informatics. Report 98–17, Delft University of Technology, TU, Delft, 1998
[11] P. Maroni, “Variations around classical orthogonal polynomials. Connected problems”, J. Comput. Appl. Math., 48 (1993), 133–155 | DOI | MR | Zbl
[12] P. Maroni, “An integral representation for the Bessel form”, J. Comp. Appl. Math., 57 (1995), 251–260 | DOI | MR | Zbl
[13] P. Maroni, M. Mejri, “Some semiclassical orthogonal polynomials of class one”, Eurasian Math. J., 2:2 (2011), 108–128 | MR | Zbl
[14] M. Mejri, “$q$-Extension of some symmetrical and semi-classical orthogonal polynomials of class one”, Appl. Anal. Discrete Math., 3 (2009), 78–87 | DOI | MR | Zbl
[15] D. S. Moak, “The $q$-analogue of the Laguerre polynomials”, J. Math. Anal. Appl., 81:1 (1981), 20–47 | DOI | MR | Zbl
[16] T. J. Stieltjes, “Recherches sur les fractions continues”, Ann. Fac. Sci. Toulouse, 8 (1894), J1–J122 ; Ann. Fac. Sci. Toulouse, 9 (1895), A1–A47 | DOI | MR | Zbl | DOI | MR