The factorization method for the general second-order q-difference equation and the Laguerre-Hahn polynomials on the general q-lattice

Journal of Physics A: Mathematical and General

Volumn 36, Issue 3, 2003, Pages 765-773

  Bangerezako, G ^a   Hounkonnou, M N ^b  

^a Fac Sciences   (Burundi)

^b U de Rech en Phys Theor   (Benin)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037462869     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/36/3/311     Document Type: Article

References (32)

1. Alvarez-Nodarse R and Costas-Santos R S 2001 The factorization method for the difference equations of hypergeometric type on nonuniform lattices J. Phys. A: Math. Gen. 34 5551-69
2. Atakishiyev N M 1984 Construction of dynamical symmetry group of the relativistic harmonic oscillator by the Infeld-Hull factorization method J. Theor. Math. Phys. 56 735-9
3. Atakishiyev N M and Suslov S K 1991 Difference analogs of the harmonic oscillator Theor. Math. Phys. 85 442-4
4. Atakishiyev N M and Suslov S K 1991 A realization of the q-harmomic oscillator Theor. Math. Phys. 87 1055-62
5. Askey R and Wilson J 1985 Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials Mem. Am. Math. Soc. 54 1-55
6. Bangerezako G 1998 Discrete Darboux transformation for discrete polynomials of hypergeometric type J. Phys. A: Math. Gen. 31 1-6
7. Bangerezako G 1999 The factorization method for the Askey-Wilson polynomials J. Comput. Appl. Math. 107 219-32
8. Bangerezako G and Magnus A P 1999 The factorization method for the semi-classical polynomials Proc. IW SSS JINR E5-99-38 (Dubna) ed V B Priezhev and V P Spiridonov pp 295-300
9. Bangerezako G and Hounkonnou M N 2001 The transformation of polynomial eigenfunctions of linear second-order difference operators: a special case of Meixner polynomials J. Phys. A: Math. Gen. 34 1-14
10. Bangerezako G 2001 The fourth order difference equation for the Laguerre-Hahn polynomials orthogonal on special non-uniform lattices Ramanujan J. 5 167-81
11. Bangerezako G and Hounkonnou M N 2002 The transformation of polynomial eigenfunctions of linear second-order difference operators: a special case of the q-Jacobi polynomials Proc. 2nd Int. Workshop on Contemporary Problems in Mathematical Physics ed J Govaerts, M N Hounkonnou and A Msezane (Singapore: World Scientific) 427-739
12. Burchnall J L and Chaundy T W 1922 Commutative ordinary differential operators I Proc. Lond. Math. Soc. 21 420-40
13. Burchnall J L and Chaundy T W 1928 Commutative ordinary differential operators II Proc. R. Soc. 118 557-83
14. Kalnins E G and Miller W 1989 Symmetry techniques for q-series: Askey-Wilson polynomials Rocky Mt. J. Math. 19 223-30
15. Darboux G 1882 Sur une proposition relative aux equations lineaires C. R. Acd. Sci., Paris 94 1456
16. Duistermaat J and Grunbaum F A 1986 Differential equations in the spectral parameter Commun. Math. Phys. 103 177-240
17. Grunbaum F A and Haine L 1996 The q-version of a theorem of Bochner J. Comput. Appl. Math. 68 103-14
18. Infeld L and Hull T 1951 The factorization method Rev. Mod. Phys. 23 21-68
19. Koekoek R and Swarttouw R 1998 The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report of Tech. Univ. Delft, Fac. Tech. Math. Inf. 98-17
20. Lorente M 2001 Raising and lowering operators, factorization method and differential/difference operators of hypergeometric type J. Phys. A: Math. Gen. 34 569-88
21. Magnus A P 1988 Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials Springer Lecture Note in Math vol 1329 (Berlin: Springer) pp 261-78
22. Miller W 1969 Lie theory and difference equations I J. Math. Anal. Appl. 28 383-99
23. Miller W 1970 Lie theory and q-difference equations SIAM J. Math. Anal. 1 171-88
24. Mielnik B 1984 Factorization method and new potentials with the oscillator spectrum J. Math. Phys. 25 3387-9
25. Nikiforov A, Suslov S and Uvarov V 1991 Classical orthogonal polynomials of a discrete variable (Berlin: Springer)
26. Oscar Rosas-Ortiz J 1998 Exactly solvable hydrogen-like potentials and factorization method J. Phys. A: Math. Gen. 31 10163-79
27. Oscar Rosas-Ortiz J 1998 On the factorization method in quantum mechanics 1st Int. Worskshop on Symmetries in Quantum Mechanics and Quantum Optics (Burgos, Spain)
28. Samsonov B and Ovcharov I 1995 Darboux transformation and non-classical orthogonal polynomials Izv. Vuzov (Fiz.) 4 58-65 (in Russian)
29. Schrödinger E 1941 Further studies on solving eigenvalue problems by factorization Proc. R. Ir. Acad. A 46 183-206
30. Smirnov Yu F 1997 On the factorization and algebraization of difference equation of hypergeometric type Proc. Int. Workshop on Orthogonal Polynomials in Mathematical Physics ed M Alfaro, R Alvarez-Nadarse, G Lagomasino and F Marcelan (Madrid: Publicaciones de la Universidad Carlos) pp 153-61
31. Smirnov Yu F 1998 Finite difference equations and factorization method Proc. 5th Wigner Symp. ed P Kasperkovitz and D Grau (Singapore: World Scientific) pp 148-150
32. Smirnov Yu F 1999 Factorization method: new aspects Rev. Mex. Fis. 45 1-6