On orthogonal polynomials with respect to the form -(x - c)S' |
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Authors: | R. Sfaxi J. Alaya |
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Affiliation: | 601. Institut Supérieur de Gestion de Gab?s, Département des Méthodes Quantitatives, Rue Jilani Habib 6002-Gab?s, Tunisia 602. Faculté des Sciences de Gab?s, Route de Mednine, 6029- Gab?s, Tunisia
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Abstract: | Summary A form (linear functional) $u$ is called regular if we can associate with it a sequence of monic orthogonal polynomials. On certain regularity conditions, the product of a non regular form by a polynomial can be regular. The purpose of this work is to establish regularity conditions of the form $-(x-c){mathbf S}',$ where ${mathbf S}$ is a classical (Bessel, Jacobi). We give the second-order recurrence relations and structure relations of its corresponding orthogonal polynomial sequence. We conclude with an example as an illustration. |
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Keywords: | orthogonal polynomials classical polynomials semi-classical forms finite-type relations coherent pairs diagonal sequences |
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