Comptes Rendus
no. 1-2
Mathematical Analysis
On m-symmetric d-orthogonal polynomials
[Sur les polynômes d-orthogonaux m-symétriques]

Présenté par : Jean-Pierre Demailly

Mongi Blel1
1 Department of Mathematics College of Science, King Saud University, Riyadh 11451, BP 2455, Saudi Arabia
Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 19-22.

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 m=d. Then we discuss, as far as we know, a new symmetric classical 3-PS.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2011.12.011
Mongi Blel 1

1 Department of Mathematics College of Science, King Saud University, Riyadh 11451, BP 2455, Saudi Arabia 
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Mongi Blel. On m-symmetric d-orthogonal polynomials. Comptes Rendus. Mathématique, Volume 350 (2012) no. 1-2, pp. 19-22. doi : 10.1016/j.crma.2011.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.12.011/

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