Geodesic
Linearization of Arbitrary products of classical orthogonal polynomials
Applicationes Mathematicae, Tome 27 (2000) no. 2, pp. 187-196.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/am-27-2-187-196
Keywords: classical orthogonal polynomials, Hermite orthogonal polynomials, linearization coefficients, recurrence relations, differential equations

Mahouton Hounkonnou 1 ; Said Belmehdi 1 ; André Ronveaux 1

1 
@article{10_4064_am_27_2_187_196,
     author = {Mahouton Hounkonnou and Said Belmehdi and Andr\'e Ronveaux},
     title = {Linearization of {Arbitrary} products of classical orthogonal polynomials},
     journal = {Applicationes Mathematicae},
     pages = {187--196},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2000},
     doi = {10.4064/am-27-2-187-196},
     zbl = {0997.33002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-27-2-187-196/}
}
TY  - JOUR
AU  - Mahouton Hounkonnou
AU  - Said Belmehdi
AU  - André Ronveaux
TI  - Linearization of Arbitrary products of classical orthogonal polynomials
JO  - Applicationes Mathematicae
PY  - 2000
SP  - 187
EP  - 196
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-27-2-187-196/
DO  - 10.4064/am-27-2-187-196
LA  - en
ID  - 10_4064_am_27_2_187_196
ER  - 
%0 Journal Article
%A Mahouton Hounkonnou
%A Said Belmehdi
%A André Ronveaux
%T Linearization of Arbitrary products of classical orthogonal polynomials
%J Applicationes Mathematicae
%D 2000
%P 187-196
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am-27-2-187-196/
%R 10.4064/am-27-2-187-196
%G en
%F 10_4064_am_27_2_187_196
Mahouton Hounkonnou; Said Belmehdi; André Ronveaux. Linearization of Arbitrary products of classical orthogonal polynomials. Applicationes Mathematicae, Tome 27 (2000) no. 2, pp. 187-196. doi : 10.4064/am-27-2-187-196. http://geodesic.mathdoc.fr/articles/10.4064/am-27-2-187-196/

Cité par Sources :