Discrete Darboux transformation for discrete polynomials of hypergeometric type

Journal of Physics A: Mathematical and General

Volumn 31, Issue 9, 1998, Pages 2191-2196

  Bangerezako, Gaspard ^a,b  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^b UNIVERSITY OF BURUNDI   (Burundi)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032489191     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/9/009     Document Type: Article

References (18)

1. Askey R and Wilson J 1985 Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials Mem. Am. Math. Soc. 54 1-55
2. Bangerezako G and Magnus A P The factorization method and the semi-classical orthogonal polynomials, in preparation
3. Darboux G 1915 Théorie des Surfaces vol II (Paris: Gauthier-Villars) p 213
4. Infeld L and Hull T 1951 The factorization method Rev. Mod. Phys. 23 21-68
5. Kalnins E G and Miller W 1989 Symmetry techniques for q-series: Askey-Wilson polynomials Rocky Mountain J. Math. 19 223-30
6. Magnus A P 1988 Associated Askey-Wilson Polynomials as Laguerre-Hahn Orthogonal Polynomials (Lecture Notes in Mathematics 1329) (Berlin: Springer) pp 261-78
7. Magnus A P 1997 Special non uniform lattice(snul) orthogonal polynomials on discrete dense sets of points J. Comput. Appl Math. 65 253-65
8. Magnus A P 1984 Riccati Acceleration of Jacobi Continued Fractions and Laguerre-Hanh Orthogonal Polynomials (Lecture Notes in Mathematics 1071) (Berlin: Springer) pp 213-30
9. Miller W Jr 1969 Lie theory and difference equations I J. Math. Anal. Appl. 28 383-99
10. Nikiforov A, Suslov S and Uvarov V 1991 Classical Orthogonal Polynomials of a Discrete Variable (Springer Series in 0omputational Physics) (Berlin: Springer)
11. Shabat A 1992 The infinite dimensional dressing dynamical system Inverse Problems 8 303-8
12. Shabat A B and Veselov A P 1993 Dressing chain and spectral theory of Schrödinger operator Funct. Anal. Appl. 27 81-96 (translation from 1993 Funk. Anal. Pril. 27 1-21)
13. Shabat A B and Veselov A P 1993 Dressing chain and spectral theory of Schrödinger operator Funct. Anal. Appl. 27 81-96 (translation from 1993 Funk. Anal. Pril. 27 1-21)
14. Smirnov Yu F 1996 On factorization and algebraization of difference equations of hypergeometric type Proc. Int. Workshop on Orthogonal Polynomials in Mathematical Physics (Leganés, 24-26 June) ed M Alfaro et al
15. Spiridonov V, Vinet L and Zhedanov A 1993 Difference Schrödinger operators with linear and exponential discrete spectra Lett. Math. Phys. 29 63-73
16. Spiridonov V, Vinet L and Zhedanov A 1995 Discrete Darboux transformations, the discrete-time Toda lattice and the Askey-Wilson polynomials Meth. Anpl. Anal. 2 369-98
17. Spiridonov V, Vinet L and Zhedanov A 1997 Spectral transformations, self-similar reductions and orthogonal polynomials J. Phys. A: Math. Gen. 30 7621-37
18. Zhedanov A 1997 Rational spectral transformations and orthogonal polynomials J. Comput. Appl. Math. 85 67-86