Autor: Belmehdi, Saïd - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Linearization of the product of orthogonal polynomials of a discrete variable
Autorzy:: Belmehdi, Saïd
Lewanowicz, Stanisław
Ronveaux, André
Powiązania:: https://bibliotekanauki.pl/articles/1339159.pdf
Data publikacji:: 1997
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: linearization coefficients
classical orthogonal polynomials of a discrete variable
recurrence relations
Opis:: 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 {$P_k$}.
Źródło:: Applicationes Mathematicae; 1996-1997, 24, 4; 445-455
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Linearization of Arbitrary products of classical orthogonal polynomials
Autorzy:: Hounkonnou, Mahouton
Belmehdi, Said
Ronveaux, André
Powiązania:: https://bibliotekanauki.pl/articles/1208207.pdf
Data publikacji:: 2000
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: classical orthogonal polynomials
Hermite orthogonal polynomials
linearization coefficients
recurrence relations
differential equations
Opis:: 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.
Źródło:: Applicationes Mathematicae; 2000, 27, 2; 187-196
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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