Discrete semi-classical orthogonal polynomials of class one on quadratic lattices

References

• R. Askey and J. Wilson, Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials, Memoirs AMS, Vol. 54–319, AMS, Providence, 1985.
   Google Scholar
• S. Belmehdi, On semi-classical linear functionals of class s=1. Classification and integral representations, Indag. Math. 3 (1992), pp. 253–275. doi: 10.1016/0019-3577(92)90035-J
   Web of Science ®Google Scholar
• A. Branquinho and M.N. Rebocho, Characterization theorem for Laguerre-Hahn orthogonal polynomials on non-uniform lattices, J. Math. Anal. Appl. 427 (2015), pp. 185–201. doi: 10.1016/j.jmaa.2015.02.044
   Web of Science ®Google Scholar
• A. Branquinho, Y. Chen, G. Filipuk, and M.N. Rebocho, A characterization theorem for semi-classical orthogonal polynomials on non uniform lattices, Appl. Math. Comput. 334 (2018), pp. 356–366.
   Web of Science ®Google Scholar
• D. Dominici and F. Marcellán, Discrete semiclassical orthogonal polynomials of class one, Pacific J. Math. 268 (2014), pp. 389–411. doi: 10.2140/pjm.2014.268.389
   Web of Science ®Google Scholar
• S. Elaydi, An Introduction to Difference Equations, 3rd ed., Undergraduate Texts in Mathematics, Springer, New York, 2005.
   Google Scholar
• G. Filipuk and M.N. Rebocho, Orthogonal polynomials on systems of non-uniform lattices from compatibility conditions, J. Math. Anal. Appl. 456 (2017), pp. 1380–1396. doi: 10.1016/j.jmaa.2017.07.059
   Web of Science ®Google Scholar
• M. Foupouagnigni, On difference equations for orthogonal polynomials on nonuniform lattices, J. Difference Equ. Appl. 14 (2008), pp. 127–174. doi: 10.1080/10236190701536199
   Web of Science ®Google Scholar
• M. Foupouagnigni, M. Kenfack Nangho, and S. Mboutngam, Characterization theorem for classical orthogonal polynomials on non-uniform lattices: the functional approach, Integral Transforms Spec. Funct. 22 (2011), pp. 739–758. doi: 10.1080/10652469.2010.546996
   Web of Science ®Google Scholar
• M.E.H. Ismail, Classical and Quantum Orthogonal Polynomials in One Variable, Vol. 98 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 2005.
   Google Scholar
• R. Koekoek and R. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Faculty of Information Technology and Systems, Delft University of Technology, Netherlands, Report no. 98–17, 1998.
   Google Scholar
• A.P. Magnus, Associated Askey-Wilson Polynomials as Laguerre-Hahn Orthogonal Polynomials, Springer Lect. Notes in Math., Vol. 1329, Springer, Berlin, 1988, pp. 261–278.
   Google Scholar
• A.P. Magnus, Painlevé-type differential equations for the recurrence coefficients of semiclassical orthogonal polynomials, J. Comput. Appl. Math. 57 (1995), pp. 215–237. doi: 10.1016/0377-0427(93)E0247-J
   Web of Science ®Google Scholar
• A.P. Magnus, Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points, J. Comput. Appl. Math. 65 (1995), pp. 253–265. doi: 10.1016/0377-0427(95)00114-X
   Web of Science ®Google Scholar
• P. Maroni and M. Mejri, The symmetric Dω-semiclassical orthogonal polynomials of class one, Numer. Algorithms 49 (2008), pp. 251–282. doi: 10.1007/s11075-008-9170-2
   Web of Science ®Google Scholar
• S. Mboutngam and M. Foupouagnigni, Characterization of semi-classical orthogonal polynomials on nonuniform lattices, Integral Transforms Spec. Funct. 29 (2018), pp. 284–309. doi: 10.1080/10652469.2018.1428583
   Web of Science ®Google Scholar
• S. Mboutngam, M. Foupouagnigni, and P. Njionou Sadjang, On the modifications of semi-classical orthogonal polynomials on nonuniform lattices, J. Math. Anal. Appl. 445 (2017), pp. 819–836. doi: 10.1016/j.jmaa.2016.06.041
   Web of Science ®Google Scholar
• A.F. Nikiforov and S.K. Suslov, Classical orthogonal polynomials of a discrete variable on non uniform lattices, Lett. Math. Phys. 11 (1986), pp. 27–34. doi: 10.1007/BF00417461
   Web of Science ®Google Scholar
• A.F. Nikiforov, S.K. Suslov, and V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
   Google Scholar
• M. NjinkeuSandjon, A. Branquinho, M. Foupouagnigni, and I. Area, Characterizations of classical orthogonal polynomials on quadratic lattices, J. Difference Equ. Appl. 23 (2017), pp. 983–1002. doi: 10.1080/10236198.2017.1307972
   Web of Science ®Google Scholar
• S.K. Suslov, On the theory of difference analogues of special functions of hypergeometric type, Usp. Mat. Nauk 4 (1989), pp. 185–226.
   Google Scholar
• G. Szegö, Orthogonal Polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc., Providence, RI, 1975.
   Google Scholar
• N.S. Witte, Semi-classical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy, Nagoya Math. J. 219 (2015), pp. 127–234. doi: 10.1215/00277630-3140952
   Web of Science ®Google Scholar
• A. Zhedanov, Rational spectral transformations and orthogonal polynomials, J. Comput. Appl. Math. 85 (1997), pp. 67–86. doi: 10.1016/S0377-0427(97)00130-1
   Web of Science ®Google Scholar