On the limit relations between classical continuous and discrete orthogonal polynomials

Journal of Computational and Applied Mathematics

Volumn 91, Issue 1, 1998, Pages 97-105

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

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSITY OF NAMUR   (Belgium)

^c UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Connection problem; Limit relation; Orthogonal polynomials

Indexed keywords

ALGORITHMS; PROBLEM SOLVING;

LIMIT RELATIONS; ORTHOGONAL POLYNOMIALS;

POLYNOMIALS;

EID: 0032051051     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00026-0     Document Type: Article

References (19)

1. [1] G.E. Andrews, R. Askey, Classical orthogonal polynomials, in: C. Brezinski et al. (eds.), Polynômes Orthogonaux et Applications, Lecture Notes in Math., Vol. 1171, Springer, Berlin, 1985, pp. 36-62.
2. [2] I. Area, E. Godoy, A. Ronveaux, A. Zarzo, Minimal recurrence relation for connection coefficients between classical orthogonal polynomials: discrete case. J. Comput. Appl. Math. 89 (1998) 309-325.
3. [3] A. Branquinho, F. Marcellán, Generating new classes of orthogonal polynomials, Internat. J. Math. Math. Sci. 19 (1996) 643-656.
4. [4] T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
5. [5] E. Godoy, I. Area, A. Ronveaux, A. Zarzo, Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: continuous case. J. Comput. Appl. Math. 84 (1997) 257-275.
6. [6] R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Fac. Techn. Math. Informatics, Delft University of Technology. Report 94-05, Delft 1994.
7. [7] F. Marcellán, A. Branquinho, J. Petronilho, Classical orthogonal polynomials: a functional approach, Acta Appl. Math. 34 (1994) 283-303.
8. [8] A.F. Nikiforov, S.K. Suslov, V.B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991.
9. [9] A.F. Nikiforov, V.B. Uvarov, Special Functions of Mathematical Physics, Birkhaüser, Basel, 1988.
10. [10] F.J.W. Olver, Asymptotics and Special Functions, Academic Press, New York and London, 1974.
11. [11] A. Ronveaux, Quasi-orthogonality and differential equations, J. Comput. Appl. Math. 29 (1990) 243-248.
12. [12] A. Ronveaux, Limit transitions in the Askey tableau, in: W. Van Assche (Ed.), Open Problems Section J. Comput. Appl. Math. 48 (1-2) (1993) 234-236.
13. [13] A. Ronveaux, A. Zarzo, E. Godoy, Recurrence relation for connection coefficients between two families of orthogonal polynomials. J. Comp. Appl. Math. 62 (1995) 67-73.
14. [14] A. Ronveaux, S. Belmchdi, E. Godoy, A. Zarzo, Recurrence relation approach for connection coefficients. Application to classical discrete orthogonal polynomials, in: D. Levi, L. Vinet, P. Winternitz (Eds.), Proc. Internat. Workshop on Symmetries and Entegrability of Difference Equations, CRM Proc. and Lecture Note Series 9, AMS, Providence, Rhode Island, 1996, pp. 321-337.
15. [15] G. Szegö, Orthogonal Polynomials A.M.S. Colloquium Publications vol. XXIII, AMS, Providence, Rhode Island, 1978.
16. [16] J.D. Talman, Special functions. A group theoretic approach. Based on lectures by E.P. Wigner and W.A. Benjamin, INC, New York-Amsterdam, 1968.
17. [17] N.Ja. Vilenkin, Special Functions and the Theory of Groups Representations, AMS, Providence, Rhode Island, 1968.
18. [18] Wolfram Research, Inc., Mathematica version 2.2, Wolfram Research Inc., Champaign, Illinois, 1993.
19. [19] A. Zarzo, I. Area, E. Godoy, A. Ronveaux, Results for some inversion problems for classical continuous and discrete orthogonal polynomials, J. Phys. A 30 (1997) L35-L40.