Combinatorics
An identity on pairs of Appell-type polynomials
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 773-778.

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,HB)=Pn(n+1α)(1x|A,AH), 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,HB)=Pn(n+1α)(1x|A,AH), qui généralise l'identité de Carlitz sur les polynômes de Bernoulli.

Received:
Accepted:
Published online:
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
@article{CRMATH_2015__353_9_773_0,
     author = {Mihoubi, Miloud and Saidi, Yamina},
     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},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2015.06.013/}
}
TY  - JOUR
AU  - Mihoubi, Miloud
AU  - Saidi, Yamina
TI  - An identity on pairs of Appell-type polynomials
JO  - Comptes Rendus. Mathématique
PY  - 2015
SP  - 773
EP  - 778
VL  - 353
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2015.06.013/
DO  - 10.1016/j.crma.2015.06.013
LA  - en
ID  - CRMATH_2015__353_9_773_0
ER  - 
%0 Journal Article
%A Mihoubi, Miloud
%A Saidi, Yamina
%T An identity on pairs of Appell-type polynomials
%J Comptes Rendus. Mathématique
%D 2015
%P 773-778
%V 353
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2015.06.013/
%R 10.1016/j.crma.2015.06.013
%G en
%F CRMATH_2015__353_9_773_0
Mihoubi, Miloud; Saidi, Yamina. 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. 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

Cited by Sources: