Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-05-16T21:42:45.428Z Has data issue: false hasContentIssue false
  • English
  • Français

Generating functions and semi-classical orthogonal polynomials

Published online by Cambridge University Press:  14 November 2011

Pascal Maroni  and
Jeannette Van Iseghem
Pascal Maroni
Affiliation:
Laboratoire d'Analyse Numérique, Université P. et M. Curie, 75252 Paris cedex 05, France
Jeannette Van Iseghem
Affiliation:
UFR de Math, Université de Lille, 59655 Villeneuve d'Ascq cedex, France
Get access Rights & Permissions [Opens in a new window]

Extract

An orthogonal family of polynomials is given, and a link is made between the special form of the coefficients of their recurrence relation and a first-order linear homogenous partial differential equation satisfied by the associated generating function. A study is also made of the semiclassical character of such families.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 5 , 1994 , pp. 1003 - 1011
Copyright
Copyright © Royal Society of Edinburgh 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Carlitz, L.. On some polynomials of Tricomi. Boll. Un. Mat. Ital. (3) 13 (1958), 58–64.Google Scholar
2Maroni, P.. Une théorie algébrique des polynômes orthogonaux. Applications aux polynômes orthogonaux semi-dassiques. IMACS 9, eds. Brezinski, C. et al. 95–130, J. C. Baltzer, 1991).Google Scholar
3Maroni, P.. Introduction à l'étude des δ polynômes orthogonaux semi-c1assiques, Pub. Lab. Ana.-Num. 8504 (Paris, Univ. P. et M. Curie CNRS, 1985).Google Scholar
4Pollaczek, F.. Systèmes de polynômes biorthogonaux qui généralised les polynômes ultra sphériques. C. R. Acad. Sci. Paris Ser. I Math. 228 (1949), 1998–2000.Google Scholar
5Pollaczek, F.. Sur une généralisation des polynômes de Jacobi, Mémorial des Sci. Math. 131 (Paris: Gauthier-Villars, 1956).Google Scholar
6Szegö, G.. On certain special sets of orthogonal polynomials. Proc. Amer. Math. Soc. 1 (1950), 731–737.CrossRefGoogle Scholar
7Van, J.Iseghem. Generating function, Recurrence relations, Differential relations. J. Comput. Appl. Math. 49 (1993) 297–303.Google Scholar