An identity on pairs of Appell-type polynomials

Miloud Mihoubi; Yamina Saidi

doi:10.1016/j.crma.2015.06.013

Combinatorics

An identity on pairs of Appell-type polynomials

Presented by: the Editorial Board

Miloud Mihoubi ¹; Yamina Saidi ¹

¹ RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria

Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 773-778.

Abstract (OV)
Résumé

In this paper, we define a sequence of polynomials $P_{n}^{(α)} (x | A, H)$ 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 $P_{n}^{(α)} (x | B, H \circ B) = P_{n}^{(n + 1 - α)} (1 - x | A, A^{'} H)$ , which generalize the Carlitz's identity on Bernoulli polynomials.

Dans ce papier, on définit une suite de polynômes $P_{n}^{(α)} (x | A, H)$ 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 $P_{n}^{(α)} (x | B, H \circ B) = P_{n}^{(n + 1 - α)} (1 - x | A, A^{'} H)$ , qui généralise l'identité de Carlitz sur les polynômes de Bernoulli.

Received: 2014-12-28
Accepted: 2015-06-16
Published online: 2015-07-22

DOI: 10.1016/j.crma.2015.06.013

Author's affiliations:

Miloud Mihoubi ¹; Yamina Saidi ¹

¹ RECITS Laboratory, Faculty of Mathematics, USTHB, P.O. Box 32, El Alia 16111, Bab-Ezzouar, Algiers, Algeria

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     title = {An identity on pairs of {Appell-type} polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {773--778},
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     number = {9},
     year = {2015},
     doi = {10.1016/j.crma.2015.06.013},
     language = {en},
}

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Miloud Mihoubi; Yamina Saidi. An identity on pairs of Appell-type polynomials. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 773-778. doi : 10.1016/j.crma.2015.06.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.013/

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