[Sur les polynômes d-orthogonaux m-symétriques]
Dans cette Note, on montre que les composantes dʼune suite d-symétrique d-orthogonale et classique sont aussi classiques. Dans le cas où la suite est d-orthogonale classique et m-symétrique, on montre que la première composante est d-orthogonale classique. On généralise ainsi les résultats de Douak et Maroni (1992) [8]. On donne à la fin de cette note un exemple dʼune nouvelle suite 3-orthogonale symétrique classique.
In this Note, we prove that all the components of a d-symmetric classical d-orthogonal are classical and in the case where the sequence is m-symmetric and d-orthogonal, we prove that the first component of an m-symmetric classical d-orthogonal is classical. That generalized the Douak and Maroni (1992) [8] results for the case . Then we discuss, as far as we know, a new symmetric classical 3-PS.
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@article{CRMATH_2012__350_1-2_19_0,
author = {Blel, Mongi},
title = {On \protect\emph{m}-symmetric \protect\emph{d}-orthogonal polynomials},
journal = {Comptes Rendus. Math\'ematique},
pages = {19--22},
publisher = {Elsevier},
volume = {350},
number = {1-2},
year = {2012},
doi = {10.1016/j.crma.2011.12.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.12.011/}
}
TY - JOUR AU - Blel, Mongi TI - On m-symmetric d-orthogonal polynomials JO - Comptes Rendus. Mathématique PY - 2012 SP - 19 EP - 22 VL - 350 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.12.011/ DO - 10.1016/j.crma.2011.12.011 LA - en ID - CRMATH_2012__350_1-2_19_0 ER -
Blel, Mongi. On m-symmetric d-orthogonal polynomials. Comptes Rendus. Mathématique, Tome 350 (2012) no. 1-2, pp. 19-22. doi : 10.1016/j.crma.2011.12.011. http://www.numdam.org/articles/10.1016/j.crma.2011.12.011/
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