Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton\n q-Bessel function

1995/02/13 by Erik Koelink, Walter Van Assche, Koelink, Erik +1
Chemistry · Materials Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Molecular spectroscopy and chirality #Nonlinear Optical Materials Research

paper · pdf · doi:10.48550/arxiv.math/9502227

openalex publication_date 1995/02/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Laurent polynomials related to the Hahn-Exton q-Bessel function, which are\nq-analogues of the Lommel polynomials, have been introduced by Koelink and\nSwarttouw. The explicit strong moment functional with respect to which the\nLaurent q-Lommel polynomials are orthogonal is given. The strong moment\nfunctional gives rise to two positive definite moment functionals. For the\ncorresponding sets of orthogonal polynomials the orthogonality measure is\ndetermined using the three-term recurrence relation as a starting point. The\nrelation between Chebyshev polynomials of the second kind and the Laurent\nq-Lommel polynomials and related functions is used to obtain estimates for\nthe latter.\n

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