Linearization of Arbitrary products of classical orthogonal polynomials

• Autorzy: Mahouton Norbert Hounkonnou , Said Belmehdi , André Ronveaux
• Języki publikacji: EN

Abstrakty

EN

A procedure is proposed in order to expand $w=\prod^N_{j=1} P_{i_j}(x)=\sum^M_{k=0} L_ k P_ k(x)$ where $P_i(x)$ belongs to aclassical orthogonal polynomial sequence (Jacobi, Bessel, Laguerre and Hermite) ($M=\sum^N_{j=1} i_j$). We first derive a linear differential equation of order $2^N$ satisfied by w, fromwhich we deduce a recurrence relation in k for the linearizationcoefficients $L_k$. We develop in detail the two cases $[P_i(x)]^N$, $P_ i(x)P_ j(x)P_ k(x)$ and give the recurrencerelation in some cases (N=3,4), when the polynomials $P_i(x)$are monic Hermite orthogonal polynomials.

Słowa kluczowe

EN

classical orthogonal polynomials; Hermite orthogonal polynomials; linearization coefficients; recurrence relations; differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 2
• Strony: 187-196

Daty

wydano

2000

otrzymano

1998-09-30

poprawiono

1999-05-18

Twórcy

autor

Mahouton Norbert Hounkonnou

• Unité de Recherche en Physique Théorique (URPT), Institut de Mathématique et de Sciences Physiques (IMSP), Université Nationale du Benin, BP 613 Porto-Novo, Benin

autor

Said Belmehdi

• UFR de Mathématique, Université des Sciences et Technologies, Lille I, F-59655 Villeneuve d'Ascq, France

autor

André Ronveaux

• Facultés Universitaires Notre-Dame de la Paix, rue de Bruxelles, 61, B-5000 Namur, Belgium

Bibliografia

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