Factorization method for difference equations of hypergeometric type on nonuniform lattices

Journal of Physics A: Mathematical and General

Volumn 34, Issue 27, 2001, Pages 5551-5569

  Alvarez Nodarse R ^a,b   Costas Santos, R S ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039845450     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/27/306     Document Type: Article

References (32)

1. 3 Integral Trans. Special Funct. 8 299-324
2. Álvarez-Nodarse R and Medem J C 2001 q-classical polynomials and the g-Askey and Nikiforov-Uvarov J. Comput. Appl. Math. at press
3. q(2) J. Phys. A: Math. Gen. 29 1435-51
4. Atakishiyev N M 1983 Construction of the dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method Group Theoretical Methods in Physics (Lecture Notes in Physics vol 180) ed M Serdaroglu and E Inonu (Berlin: Springer) pp 393-6 Atakishiyev N M 1984 Theor. Math. Phys. 56 563-72
5. Atakishiyev N M 1983 Construction of the dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method Group Theoretical Methods in Physics (Lecture Notes in Physics vol 180) ed M Serdaroglu and E Inonu (Berlin: Springer) pp 393-6 Atakishiyev N M 1984 Theor. Math. Phys. 56 563-72
6. Askey R and Suslov S K 1993 The q-harmonic oscillator and the Al-Salam and Carlitz polynomials Lett. Math. Phys. 29 123-32
7. Atakishiyev N M and Wolf B 1994 Approximation on a finite set of points through Kravchuk functions Rev. Mex. Fis. 40 1055-62
8. Atakishiyev N M, Rahman M and Suslov S K 1995 On classical orthogonal polynomials Constructive Approx. 11 181-226
9. Atakishiyev N M and Suslov S K 1991 Difference analogs of the harmonic oscillator Theor. Math. Phys. 85 442-4
10. Atakishiyev N M and Suslov S K 1991 A realization of the q-harmonic oscillator Theor. Math. Phys. 87 1055-62
11. Atakishiyev N M, Frank A and Wolf K B 1994 A simple difference realization of the Heisenberg g-algebra J. Math. Phys. 35 3253-60
12. Bangerezako G 1998 Discrete Darboux transformation for discrete polynomials of hypergeometric type J. Phys. A: Math. Gen. 31 2191-6
13. Bangerezako G 1999 The factorization method for the Askey-Wilson polynomials J. Comput. Appl. Math. 107 219-32
14. q(2) and a q-analogue of the boson operators J. Phys. A: Math. Gen. 22 L873-8
15. Darboux G Théorie des Surfaces vol 2 (Paris: Gauthier-Villars)
16. Gasper G and Rahman M 1990 Basic Hypergeometric Series (Cambridge: Cambridge University Press)
17. Infeld L and Hull T E 1951 The factorization method Rev. Mod. Phys. 23 21-68
18. Koekoek R and Swarttouw R F 1998 The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Reports of the Faculty of Technical Mathematics and Informatics No 98-17 Delft, Delft University of Technology
19. Lorente M 2001 Raising and lowering operators, factorization method and differential/difference operators of hypergeometric type J. Phys. A: Math. Gen. 34 569-88
20. q(2) J. Phys. A: Math. Gen. 22 4581-8
21. Miller W Jr 1969 Lie theory and difference equations. I J. Math. Anal. Appl. 28 383-99
22. Miller W Jr 1970 Lie theory and q-difference equations SIAM J. Math. Anal. 1 171-88
23. Nagiyev Sh M 1995 Difference Schrödinger equation and Q-oscillator model Theor. Math. Phys. 102 180-7
24. Nikiforov A F, Suslov S K and Uvarov V B 1991 Classical orthogonal polynomials of a discrete variable (Springer Series in Computational Physics) (Berlin: Springer)
25. Nikiforov A F and Uvarov VB 1993 Polynomial solutions of hypergeometric type difference equations and their classification Integral Trans. Special Funct. 1 223-49
26. Schrödinger E 1940 A method of determining quantum-mechanical eigenvalues and eigenfunctions Proc. R. Irish. Acad. A 46 9-16
27. Schrödinger E 1941 The factorization of the hypergeometric equation Proc. R. Irish. Acad. A 47 53-4
28. Smirnov Yu F 1997 On factorization and algebraization of difference equation of hypergeometric type Proc. Int. Workshop on Orthogonal Polynomials in Mathematical Physics ed M Alfaro et al pp 153-61 (Servicio de Publicaciones de la Universidad Carlos III de Madrid)
29. Smirnov Yu F 1998 Finite difference equations and factorization method Proc. 5th Wigner Symp. ed P Kasperkovitz and D Grau (Singapore: World Scientific) pp 148-50
30. Smirnov Yu F 1999 Factorization method: new aspects Rev. Mex. Fis. 45 1-6
31. Spiridonov V, Vinet L and Zhedanov A 1993 Difference Schrödinger operators with linear and exponential discrete spectra Lett. Math. Phys. 29 63-73
32. Vilenkin N Ja and Klimyk A U 1992 Representations of Lie Groups and Special Functions vols 1-3 (Dordrecht: Kluwer)