Hypergeometric type q-difference equations: Rodrigues type representation for the second kind solution

Journal of Computational and Applied Mathematics

Volumn 173, Issue 1, 2005, Pages 81-92

  Area, I ^a   Godoy, E ^a   Ronveaux, A ^b   Zarzo, A ^c,d  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c UNIVERSITY OF GRANADA   (Spain)

^d UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Functions of the second kind; Orthogonal polynomials; Second order q difference equations of hypergeometric type

Indexed keywords

FUNCTIONS; INTEGRAL EQUATIONS; POLYNOMIALS;

FUNCTIONS OF THE SECOND KIND; INTEGRALS; ORTHOGONAL POLYNOMIALS; SECOND-ORDER Q-DIFFERENCE EQUATIONS OF HYPERGEOMETRIC TYPE;

DIFFERENCE EQUATIONS;

EID: 27744529558     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.02.018     Document Type: Article

References (23)

1. G.E. Andrews, R. Askey, R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge, 2000.
2. I. Area, E. Godoy, A. Ronveaux, and A. Zarzo Inversion problems in the q-Hahn tableau J. Symbolic Comput 28 1999 767 776
3. I. Area, E. Godoy, A. Ronveaux, and A. Zarzo Hypergeometric type differential equations second kind solutions and related integrals J. Comput. Appl. Math 157 2003 93 106
4. N.M. Atakishiyev, M. Rahman, and S.K. Suslov On classical orthogonal polynomials Constructive Approx 11 1995 181 223
5. P.M. Batchelder An Introduction to Linear Difference Equations 1967 Dover New York
6. M. Foupouagnigni, A. Ronveaux, and W. Koepf Fourth order q-difference equation for the first associated of the q-classical orthogonal polynomials J. Comput. Appl. Math 101 1999 231 236
7. G. Gasper, and M. Rahman Basic Hypergeometric Series 1990 Cambridge University Press Cambridge
8. A. Gupta On a q-extension of "incomplete" beta function J. Indian Math. Soc. (N.S.) 66 1 4 1999 193 201
9. W. Hahn Über orthogonalpolynome, q-differenzengleichungen genügen Math. Nachr 2 1949 4 34
10. E.L. Ince Ordinary Differential Equations 1965 Dover New York
11. M.E.H. Ismail, and P. Simeonov A fourth order q-difference equation for associated discrete q-orthogonal polynomials J. Math 32 2 2002 679 690
12. F.H. Jackson q-Definite integrals, Quart J. Pure Appl. Math 41 15 1910 193 203
13. F.H. Jackson The q-integral analogous to Borel's integral Mess. Math 47 1917 57 64
14. V. Kac, and P. Cheung Quantum Calculus 2002 Springer New York
15. W.G. Kelley, and A.C. Peterson Difference Equations 1991 Academic Press San Diego
16. R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report 98-17, Fac. Techn. Math. Informatics, Delft University of Technology, Delft, 1998.
17. T. Koornwinder, Compact quantum groups and q-special functions, in: V. Baldoni, M.A. Picardello (Eds.), Representations of Lie Groups and Quantum Groups, Pitman Research Notes in Mathematics Series, Vol. 311, Longman Scientific & Technical, New York, 1994, pp. 46-128.
18. S. Lewanowicz Representation for the first associated q-classical orthogonal polynomials J. Comput. Appl. Math 150 2003 311 327
19. A.F. Nikiforov, V.B. Ouvarov, Eléments de la Théorie des Fonctions Spéciales, Mir, Moscou, 1974.
20. A.F. Nikiforov, S.K. Suslov, and V.B. Uvarov Classical Orthogonal Polynomials of a Discrete Variable, Springer Series in Computational Physics 1991 Springer Berlin
21. A.F. Nikiforov, and V.B. Uvarov Special Functions of Mathematical Physics A unified Introduction with Applications 1988 Birkhäuser, Basel Boston
22. B.O. Rodrigues, Mémoire sur l'attraction des sphéroïdes, Correspondance sur l'Ecole Royale Polytechnique T, III, Paris, 1816, pp. 361-385.
23. S.K. Suslov The theory of difference analogues of special functions of hypergeometric type Russian Math. Surveys 44 2 1989 227 278