Geodesic
Combinatorics
An identity on pairs of Appell-type polynomials
[Une identité sur des paires de polynômes de type Appell]

Présenté par : the Editorial Board

Mihoubi, Miloud1 ; Saidi, Yamina1
1 RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria
Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 773-778.

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In this paper, we define a sequence of polynomials Pn(α)(x|A,H) depending only on the choice of two analytic functions A and H in a neighborhood of zero. For a pair of compositional inverses A and B, we will show the identity Pn(α)(x|B,H∘B)=Pn(n+1−α)(1−x|A,A′H), which generalize the Carlitz's identity on Bernoulli polynomials.

Dans ce papier, on définit une suite de polynômes Pn(α)(x|A,H) dépendant seulement du choix de deux fonctions analytiques dans un voisinage de zéro. Pour une paire de fonctions réciproques A et B, on montre l'identité Pn(α)(x|B,H∘B)=Pn(n+1−α)(1−x|A,A′H), qui généralise l'identité de Carlitz sur les polynômes de Bernoulli.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.06.013

Mihoubi, Miloud 1 ; Saidi, Yamina 1

1 RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria 
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Mihoubi, Miloud; Saidi, Yamina. An identity on pairs of Appell-type polynomials. Comptes Rendus. Mathématique, Tome 353 (2015) no. 9, pp. 773-778. doi : 10.1016/j.crma.2015.06.013. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.06.013/

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