Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function
Classical Analysis and ODEs
2009-09-25 v1
Abstract
Laurent polynomials related to the Hahn-Exton -Bessel function, which are -analogues of the Lommel polynomials, have been introduced by Koelink and Swarttouw. The explicit strong moment functional with respect to which the Laurent -Lommel polynomials are orthogonal is given. The strong moment functional gives rise to two positive definite moment functionals. For the corresponding sets of orthogonal polynomials the orthogonality measure is determined using the three-term recurrence relation as a starting point. The relation between Chebyshev polynomials of the second kind and the Laurent -Lommel polynomials and related functions is used to obtain estimates for the latter.
Cite
@article{arxiv.math/9502227,
title = {Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function},
author = {Erik Koelink and Walter Van Assche},
journal= {arXiv preprint arXiv:math/9502227},
year = {2009}
}