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
[Une identité sur des paires de polynômes de type Appell]

Présenté par : 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.

Résumé
Abstract

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.

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.

Reçu le : 2014-12-28
Accepté le : 2015-06-16
Publié le : 2015-07-22

DOI : 10.1016/j.crma.2015.06.013

Affiliations des auteurs :

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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     author = {Miloud Mihoubi and Yamina Saidi},
     title = {An identity on pairs of {Appell-type} polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {773--778},
     publisher = {Elsevier},
     volume = {353},
     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/

Bibliographie
Cité par

[1] E.T. Bell Exponential polynomials, Ann. Math., Volume 35 (1934), pp. 258-277

[2] L. Carlitz; Degenerate Stirling Bernoulli and Eulerian numbers, Util. Math., Volume 15 (1979), pp. 51-88

[3] L. Comtet Advanced Combinatorics, D. Reidel Publishing Company, Dordrecht, the Netherlands/Boston, USA, 1974

[4] D.C. Kurtz A note on concavity properties of triangular arrays of numbers, J. Comb. Theory, Ser. A, Volume 13 (1972), pp. 135-139

[5] M. Mihoubi Bell polynomials and binomial type sequences, Discrete Math., Volume 308 (2008), pp. 2450-2459

[6] T.R. Prabhakar; Sharda Gupta Bernoulli polynomials of the second kind and general order, Indian J. Pure Appl. Math., Volume 11 (1980) no. 10, pp. 1361-1368

[7] S. Roman The Umbral Calculus, Dover Publ. Inc., New York, 2005

[8] P. Tempesta On Appell sequences of polynomials of Bernoulli and Euler type, J. Math. Anal. Appl., Volume 341 (2008), pp. 1295-1310

[9] R. Tremblay; S. Gaboury; B.-J. Fugère A new class of generalized Apostol–Bernoulli polynomials and some analogues of the Srivastava–Pintér addition theorem, Appl. Math. Lett., Volume 24 (2011), pp. 1888-1893

[10] W. Wang Generalized higher order Bernoulli number pairs and generalized Stirling number pairs, J. Math. Anal. Appl., Volume 364 (2010), pp. 255-274

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