no. 9
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.

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.

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.

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://www.numdam.org/articles/10.1016/j.crma.2015.06.013/

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

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

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

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

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

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

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

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

[9] Tremblay, R.; Gaboury, S.; Fugère, B.-J. 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] Wang, W. 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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