Linearization of the product of orthogonal polynomials of a discrete variable

• Autorzy: Saïd Belmehdi , Stanisław Lewanowicz , André Ronveaux
• Języki publikacji: EN

Abstrakty

EN

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 $P_iP_j=\sum_kc(i,j,k)P_k$, 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 {$P_k$}.

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1996-1997
• Tom: 24
• Numer: 4
• Strony: 445-455

Daty

wydano

1997

otrzymano

1996-11-07

Twórcy

autor

Saïd Belmehdi

• UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq, France

autor

Stanisław Lewanowicz

• Institute of Computer Science, University of Wrocław, 51-151 Wrocław, Poland

autor

André Ronveaux

• Laboratoire de Physique Mathématique Facultés Universitaires N.-D. de la Paix, B-5000 Namur, Belgium

Bibliografia

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• S. Lewanowicz, Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable, ibid. 76 (1996), 213-229.
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• A. Ronveaux, S. Belmehdi, E. Godoy and A. Zarzo, Recurrence relations approach for connection coefficients-Applications to classical discrete orthogonal polynomials, in: Symmetries and Integrability of Difference Equations, D. Levi, L. Vinet and P. Winternitz (eds.), Centre de Recherches Mathématiques, CRM Proc. and Lecture Notes Ser. 9, Amer. Math. Soc., Providence, 1996, 321-337.