Given two sequences of monic orthogonal polynomials $\{P_{n}\}_{_{n\geq 0}}$ and
$\{B_{n}\}_{_{n\geq 0}}$ such that $B_{2n}(x)=P_{n}(x^{2}),n\geq0,$ we show that the Laguerre-Hahn character of one of them remains
valid for the other. Then we give relations between their classes
and the coefficients of their structure relations. As an application,
with an appropriate choice of the sequence
$\{P_{n}\}_{n\geq 0},$ we obtain a new nonsymmetric semi-classical
sequence of polynomials $\{B_{n}\}_{_{n\geq 0}}$ of class $s=1$.
Publié le : 2010-08-15
Classification:
Orthogonal polynomials,
symmetric linear functionals,
three term recurrence relation,
Laguerre-Hahn polynomials,
structure relation,
33C45,
42C05
@article{1290608192,
author = {Bouras, B. and Marcellan, F.},
title = {Quadratic decomposition of a Laguerre-Hahn polynomial sequence I},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 641-659},
language = {en},
url = {http://dml.mathdoc.fr/item/1290608192}
}
Bouras, B.; Marcellan, F. Quadratic decomposition of a Laguerre-Hahn polynomial sequence I. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 641-659. http://gdmltest.u-ga.fr/item/1290608192/