References
- Marcellán F, Moreno–Balcázar JJ. What is…a Sobolev orthogonal polynomial? Notices Am Math Soc. 2017;64(8):873–875. doi: https://doi.org/10.1090/noti1562
- Bavinck H. On polynomials orthogonal with respect to an inner product involving differences. J Comput Appl Math. 1995;57:17–27. doi: https://doi.org/10.1016/0377-0427(93)E0231-A
- Bavinck H. On polynomials orthogonal with respect to an inner product involving differences (the general case). Appl Anal. 1995;59:233–240. doi: https://doi.org/10.1080/00036819508840402
- Costas-Santos R, Soria-Lorente A. Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials. J Differ Equ Appl. 2018;24:1715–1733. doi: https://doi.org/10.1080/10236198.2018.1517760
- Huertas EJ, Soria-Lorente A. New analytic properties of nonstandard Sobolev-type Charlier orthogonal polynomials. Numer Algorithms. 2019;82(1):41–68. doi: https://doi.org/10.1007/s11075-018-0593-0
- Lewis DC. Polynomial least square approximations. Am J Math. 1947;69:273–278. doi: https://doi.org/10.2307/2371851
- Althammer P. Eine erweiterung des orthogonalitätsbegriffes bei polynomen und deren anwendung auf die beste approximation. J Reine Angew Math. 1962;211:192–204.
- Marcellán F, Xu Y. On Sobolev orthogonal polynomials. Expo Math. 2015;33:308–352. doi: https://doi.org/10.1016/j.exmath.2014.10.002
- Magnus AP. Associated Askey–Wilson polynomials as Laguerre–Hahn orthogonal polynomials. Berlin: Springer; 1988. p. 261–278. (Springer Lect. Notes in Math.; 1329).
- Magnus AP. Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points. J Comput Appl Math. 1995;65:253–265. doi: https://doi.org/10.1016/0377-0427(95)00114-X
- Nikiforov AF, Suslov SK, Uvarov VB. Classical orthogonal polynomials of a discrete variable. Berlin: Springer; 1991.
- Nikiforov AF, Uvarov VB. Special functions of mathematical physics: a unified introduction with applications. Basel: Birkhäuser; 1988.
- Hahn W. Über orthogonalpolynome, die q-differenzengleichungen genügen. Math Nachr. 1949;2:4–34. doi: https://doi.org/10.1002/mana.19490020103
- Askey R, Wilson J. Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Providence: AMS; 1985. (Memoirs AMS; vol. 54).
- Andrews GE, Askey R. Classical orthogonal polynomials. In: Brezinski C, et al., editors. Polynômes orthogonaux et applications, Proceedings, Bar-le-Duc 1984. Berlin, Springer; 1985. p. 36–62. (Lecture Notes Math; 1171).
- Gautschi W. Orthogonal polynomials: computation and approximation. New York: Oxford University Press; 2004.
- Marcellán F, Alvarez-Nodarse R. On the “Favard theorem” and its extensions. J Comput Appl Math. 2001;127:231–254. doi: https://doi.org/10.1016/S0377-0427(00)00497-0
- Mboutngam S, Foupouagnigni M. Characterization of semi-classical orthogonal polynomials on nonuniform lattices. Integr Transf Spec F. 2018;29:284–309. doi: https://doi.org/10.1080/10652469.2018.1428583
- Branquinho A, Chen Y, Filipuk G, et al. A characterization theorem for semi-classical orthogonal polynomials on non uniform lattices. Appl Math Comput. 2018;334:356–366.
- Álvarez-Nodarse R, Petronilho J. On the Krall-type discrete polynomials. J Math Anal Appl. 2004;295:55–69. doi: https://doi.org/10.1016/j.jmaa.2004.02.042
- Atakishiev NM, Rahman M, Suslov SK. On classical orthogonal polynomials. Construct Approx. 1995;11:181–226. doi: https://doi.org/10.1007/BF01203415
- Foupouagnigni M, Kenfack Nangho M, Mboutngam S. Characterization theorem for classical orthogonal polynomials on non-uniform lattices: the functional approach. Integr Transf Spec F. 2011;22:739–758. doi: https://doi.org/10.1080/10652469.2010.546996
- Branquinho A, Rebocho MN. Characterization theorem for Laguerre–Hahn orthogonal polynomials on non-uniform lattices. J Math Anal Appl. 2015;427:185–201. doi: https://doi.org/10.1016/j.jmaa.2015.02.044
- Chihara TS. An introduction to orthogonal polynomials. New York: Gordon and Breach; 1978.
- Szegö G. Orthogonal polynomials. 4th ed. Providence: Amer. Math. Soc.; 1975. (Amer. Math. Soc. Colloq. Publ.; 23).
- Nikiforov AF, Suslov SK. Classical orthogonal polynomials of a discrete variable on non uniform lattices. Lett Math Phys. 1986;11:27–34. doi: https://doi.org/10.1007/BF00417461
- Mboutngama S, Foupouagnigni M, Njionou Sadjang P. On the modifications of semi-classical orthogonal polynomials on nonuniform lattices. J Math Anal Appl. 2017;445:819–836. doi: https://doi.org/10.1016/j.jmaa.2016.06.041
- Witte NS. Semi-classical orthogonal polynomial systems on nonuniform lattices deformations of the Askey table, and analogues of isomonodromy. Nagoya Math J. 2015;219:127–234. doi: https://doi.org/10.1215/00277630-3140952
- Filipuk G, Rebocho MN. Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions. J Math Anal Appl. 2017;456:1380–1396. doi: https://doi.org/10.1016/j.jmaa.2017.07.059
- Filipuk G, Rebocho MN. Discrete semi-classical orthogonal polynomials of class one on quadratic lattices. J Differ Equ Appl. 2019;25:1–20. doi: https://doi.org/10.1080/10236198.2018.1551379
- Koekoek R, Swarttouw R. The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Faculty of Information Technology and Systems. Netherlands: Delft University of Technology; 1998. (no. 98-17).