Lowering operators associated with D-Laguerre–Hahn polynomials

Autor:	Francisco Marcellán, Ridha Sfaxi
Rok vydání:	2011
Předmět:	Classical orthogonal polynomials Discrete mathematics Difference polynomials Applied Mathematics Discrete orthogonal polynomials Orthogonal polynomials Wilson polynomials Hahn polynomials Laguerre polynomials Elementary symmetric polynomial Analysis Mathematics
Zdroj:	Integral Transforms and Special Functions. 22:879-893
ISSN:	1476-8291 1065-2469
DOI:	10.1080/10652469.2010.542576
Popis:	In this paper, a new lowering operator D u with a linear functional u as a parameter is introduced in the linear space ℙ of all polynomials in one variable with complex coefficients. It is given by The concept of D u -semiclassical polynomial sequence is defined. We show that such a sequence belongs to the family of D-Laguerre–Hahn polynomials. This allows us to provide some characterizations of a D u -semiclassical polynomial sequence in terms of a distributional equation that the linear functional satisfies as well as a structure relation. An illustrative example is considered.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ea26f0f4a3d6f2acc254c42b9c70502f https://doi.org/10.1080/10652469.2010.542576 Zobrazit plný text záznamu