- 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