L. Khériji, P. Maroni, “On the natural <nobr>$q$</nobr>-analogues of the classical orthogonal polynomials”, Eurasian Math. J., 2013, Volume 4, Number 2,Pages <nobr>82

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On the natural $q$-analogues of the classical orthogonal polynomials

L. Khériji^a, P. Maroni^b

^a Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Rue Omar Ibn El Khattab, 6072-Gabès, Tunisia
^b UMR 7598 Laboratoire Jacques-Luis Lions, Université Pierre et Marie Curie Paris 6, CNRS, Boite courrier 187, 75252 Paris cedex 05, France

Abstract: We study the natural $q$-analogues of the Hermite, Laguerre, Jacobi and Bessel $D$-classical forms. Their moments and their discrete measure and integral representations are given.

Keywords and phrases: $q$-derivative operator, $q$-classical forms, integral representation, discrete measure.

MSC: 33C45, 42C05

Received: 25.05.2011

Language: English