Classical orthogonal polynomials via a second-order linear differential operators

Baghdadi Aloui () and Wathek Chammam ()
Additional contact information
Baghdadi Aloui: Majmaah University
Wathek Chammam: Majmaah University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 689-703

Abstract: Abstract Let Tc := D(x - c)((x - c)D + 2II) be a second-order linear differential operator, where c is an arbitrary complex number, $$D: = \frac{d}{{dx}}$$D:=ddx and II represents the identity on the linear space of polynomials with complex coefficients. The aim of this paper is to describe all of the Tc-classical orthogonal polynomials. Two canonical situations appear: the Laguerre $$\{L_n^{(2)}\}_{n\geq0}$${Ln(2)}n≥0 and the Jacobi $$\{P_n^{(\alpha-2,2)}\}_{n\geq0}$${Pn(α-2,2)}n≥0

Keywords: Orthogonal polynomials; quasi-definite linear functionals; classical polynomials; differential operators; structure relations; 33C45; 42C05 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-020-0424-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:51:y:2020:i:2:d:10.1007_s13226-020-0424-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-020-0424-6

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().