This article is cited in 11 papers

Some semiclassical orthogonal polynomials of class one

P. Maroni^a, M. Mejri<sup>b

a</sup> UMR 7598 Laboratorie Jacques-Louis Lions, Université Pierre et Marie Curie Paris 6, CNRS, Paris, France
^b Institut Supérieur des Sciences Appliquées et de Technologie de Gabès, Gabès, Tunisia

Abstract: In this work, we will solve the Laguerre-Freud equations for the recurrence coefficients of the semiclassical orthogonal polynomials of class one in a particular case. The integral representation and, as a consequence, the moments of the corresponding form are obtained. Furthermore, both the characteristic elements of the structure relation and of the second-order differential equation are explicitly given.

Keywords and phrases: semiclassical orthogonal polynomials, differential equations.

MSC: 42C05, 33C45

Received: 05.03.2011

Language: English

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