A new approach to the asymptotics of Sobolev type orthogonal polynomials

Journal of Approximation Theory

Volumn 163, Issue 4, 2011, Pages 460-480

  Alfaro, M ^a   Moreno Balcazar J J ^b   Pena A ^a   Rezola, M L ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b UNIVERSITY OF ALMERÍA   (Spain)

Author keywords

Asymptotics; Bessel functions; Laguerre and Hermite polynomials; Mehler Heine type formulas; Zeros

Indexed keywords

EID: 79952190001     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2010.11.005     Document Type: Article

References (17)

1. Alfaro M., Álvarez de Morales M., Rezola M.L. Orthogonality of the Jacobi polynomials with negative parameters. J. Comput. Appl. Math. 2002, 145:379-386.
2. Alfaro M., López G., Rezola M.L. Some properties of zeros of Sobolev-type orthogonal polynomials. J. Comput. Appl. Math. 1996, 69:171-179.
3. Alfaro M., Moreno-Balcázar J.J., Peña A., Rezola M.L. Asymptotics for a generalization of Hermite polynomials. Asymptot. Anal. 2010, 66:103-117.
4. Álvarez-Nodarse R., Moreno-Balcázar J.J. Asymptotic properties of generalized Laguerre orthogonal polynomials. Indag. Math. (N.S.) 2004, 15:151-165.
5. Chihara T.S. An Introduction to Orthogonal Polynomials 1978, Gordon & Breach, New York.
6. Dueñas H., Marcellán F. The Laguerre-Sobolev-type orthogonal polynomials. J. Approx. Theory 2010, 162:421-440.
7. Gonchar A.A. On the convergence of Padé approximants for certain classe of meromorphic functions. Math. USSR Sb. 1975, 26:555-575.
8. Klambauer G. Aspects of Calculus 1986, Springer-Verlag, New York.
9. Koekoek R., Meijer H.G. A generalization of Laguerre polynomials. SIAM J. Math. Anal. 1993, 24:768-782.
10. Kuijlaars A.B.J., Martínez-Finkelshtein A., Orive R. Orthogonality of Jacobi polynomials with general parameters. Electron. Trans. Numer. Anal. 2005, 19:1-17.
11. Kuijlaars A.B.J., McLaughlin K.T.-R. Riemann-Hilbert analysis for Laguerre polynomials with large negative parameter. Comput. Methods Funct. Theory 2001, 1:205-233.
12. Kwon K.H., Littlejohn L.L. The orthogonality of the Laguerre polynomials {Ln(-k)(x)} for a positive integer k. Ann. Numer. Math. 1995, 2:289-304.
13. Kwon K.H., Littlejohn L.L., Yoon G.J. Ghost matrices and a characterization of symmetric Sobolev bilinears forms. Linear Algebra Appl. 2009, 431:104-119.
14. López Lagomasino G., Marcellán F., Van Assche W. Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product. Constr. Approx. 1995, 11:107-137.
15. Marcellán F., Moreno-Balcázar J.J. Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports. Acta Appl. Math. 2006, 94:163-192.
16. Riordan J. Combinatorial Identities 1968, Wiley, New York.
17. Szego{double acute} G. Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. 1975, vol. 23. Amer. Math. Soc., Providence RI. fourth ed.