Linearization of the product of orthogonal polynomials of a discrete variable

Saïd Belmehdi; Stanisław Lewanowicz; André Ronveaux

ArticleOriginal scientific text

Title

Linearization of the product of orthogonal polynomials of a discrete variable

Authors ¹, ², ³

Affiliations

UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France
Institute of Computer Science, University of Wrocław, 51-151 Wrocław, Poland
Laboratoire de Physique Mathématique Facultés Universitaires N.-D. de la Paix, B-5000 Namur, Belgium

Abstract

Let {

P_{k}

} be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in

P_{i} P_{j} = \sum_{k} c (i, j, k) P_{k}

, in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by {

P_{k}

}.

Keywords

ENG

linearization coefficients, classical orthogonal polynomials of a discrete variable, recurrence relations

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Title

Linearization of the product of orthogonal polynomials of a discrete variable

Affiliations

Abstract

Keywords

Bibliography