Δ-Sobolev orthogonal polynomials of Meixner type: Asymptotics and limit relation

Journal of Computational and Applied Mathematics

Volumn 178, Issue 1-2 SPEC. ISS., 2005, Pages 21-36

  Area, I ^a   Godoy, E ^a   Marcellan F ^b   Moreno Balcazar J J ^c,d  

^a UNIVERSITY OF VIGO   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^c UNIVERSITY OF ALMERÍA   (Spain)

^d UNIVERSITY OF GRANADA   (Spain)

Author keywords

coherent pairs; Asymptotics; Linear functionals; Meixner polynomials; Orthogonal polynomials; Sobolev orthogonal polynomials

Indexed keywords

ASYMPTOTIC STABILITY; FUNCTIONS; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; SET THEORY; THEOREM PROVING;

LAGUERRE POLYNOMIALS; MEIXNER LINEAR FUNCTIONAL; MEIXNER POLYNOMIALS; ORTHOGONAL POLYNOMIALS; SOBOLEV ORTHOGONAL POLYNOMIALS;

POLYNOMIALS;

EID: 14844367096     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2004.08.008     Document Type: Article

References (16)

1. M. Alfaro J.J. Moreno-Balcázar M.L. Rezola Laguerre-Sobolev orthogonal polynomials: Asymptotics for coherent pairs of type II J. Approx. Theory 122 2003 79-96
2. I. Area E. Godoy F. Marcellán Classification of all Δ-coherent pairs Integral Transforms Special Functions 9 1 2000 1-18
3. I. Area E. Godoy F. Marcellán Inner products involving differences: The Meixner-Sobolev polynomials J. Difference Equations Appl. 6 2000 1-31
4. I. Area E. Godoy F. Marcellán Δ-coherent pairs and orthogonal polynomials of a discrete variable Integral Transforms Special Functions 14 1 2003 31-57
5. I. Area E. Godoy F. Marcellán J.J. Moreno-Balcázar Ratio and Plancherel-Rotach asymptotics for Meixner-Sobolev polynomials J. Comput. Appl. Math. 116 1 1999 63-75
6. I. Area E. Godoy A. Ronveaux A. Zarzo Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: discrete case J. Comput. Appl. Math. 89 2 1998 309-325
7. H. Bavinck On polynomials orthogonal with respect to an inner product involving differences J. Comput. Appl. Math. 57 1995 17-27
8. H. Bavinck On polynomials orthogonal with respect to an inner product involving differences (The general case) Appl. Anal. 59 1995 233-240
9. H. Bavinck R. Koekoek Difference operators with Sobolev-type Meixner polynomials as eigenfunctions Comput. Math. Appl. 36 10-12 1998 163-177
10. T.S. Chihara An Introduction to Orthogonal Polynomials 1978 Gordon and Breach New York
11. A.G. García F. Marcellán L. Salto A distributional study of discrete classical orthogonal polynomials J. Comput. Appl. Math. 57 1995 147-162
12. A. Iserles P.E. Koch S.P. Nørsett J.M. Sanz-Serna On polynomials orthogonal with respect to certain Sobolev inner products J. Approx. Theory 65 2 1991 151-175
13. A. Martínez-Finkelshtein Analytic aspects of Sobolev orthogonality revisited J. Comput. Appl. Math. 127 2001 255-266
14. H.G. Meijer Determination of all coherent pairs J. Approx. Theory 89 3 1997 321-343
15. H.G. Meijer T.E. Pérez M.A. Piñar Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type J. Math. Anal. Appl. 245 2 2000 528-546
16. A.F. Nikiforov S.K. Suslov V.B. Uvarov Classical Orthogonal Polynomials of a Discrete Variable 1991 Springer Berlin