Comptes Rendus
Combinatorics/Number theory
Some applications of the r-Whitney numbers
[Quelques applications des nombres r-Whitney]
Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 965-969.

Le but de ce papier est de présenter une application des nombres r-Whitney aux valeurs des polynômes de Bernoulli et d'Euler aux points rationnels. Les résultats obtenus généralisent les formules connues des nombres de Bernoulli des deux espèces.

The main object of this paper is to give an application of the r-Whitney numbers to the values at rational arguments of the high-order Bernoulli and Euler polynomials. The obtained formulas generalize the known formulas of the Bernoulli numbers of both kinds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.08.001
Miloud Mihoubi 1 ; Meriem Tiachachat 1

1 Faculty of Mathematics, RECITS's laboratory, USTHB, PB 32, El Alia, 16111 Algiers, Algeria
@article{CRMATH_2014__352_12_965_0,
     author = {Miloud Mihoubi and Meriem Tiachachat},
     title = {Some applications of the {\protect\emph{r}-Whitney} numbers},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {965--969},
     publisher = {Elsevier},
     volume = {352},
     number = {12},
     year = {2014},
     doi = {10.1016/j.crma.2014.08.001},
     language = {en},
}
TY  - JOUR
AU  - Miloud Mihoubi
AU  - Meriem Tiachachat
TI  - Some applications of the r-Whitney numbers
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 965
EP  - 969
VL  - 352
IS  - 12
PB  - Elsevier
DO  - 10.1016/j.crma.2014.08.001
LA  - en
ID  - CRMATH_2014__352_12_965_0
ER  - 
%0 Journal Article
%A Miloud Mihoubi
%A Meriem Tiachachat
%T Some applications of the r-Whitney numbers
%J Comptes Rendus. Mathématique
%D 2014
%P 965-969
%V 352
%N 12
%I Elsevier
%R 10.1016/j.crma.2014.08.001
%G en
%F CRMATH_2014__352_12_965_0
Miloud Mihoubi; Meriem Tiachachat. Some applications of the r-Whitney numbers. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 965-969. doi : 10.1016/j.crma.2014.08.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.001/

[1] H. Belbachir; I.E. Bousbaa Translated Whitney and r-Whitney numbers: a combinatorial approach, J. Integer Seq., Volume 16 (2013) no. 8 (article 13.8.6)

[2] M. Benoumhani On Whitney numbers of Dowling lattices, Discrete Math., Volume 159 (1996), pp. 13-33

[3] A.Z. Broder The r-Stirling numbers, Discrete Math., Volume 49 (1984), pp. 241-259

[4] G.-S. Cheon; J.-H. Jung The r-Whitney numbers of Dowling lattices, Discrete Math., Volume 312 (2012) no. 15, pp. 2337-2348

[5] T.A. Dowling A class of gemometric lattices bases on finite groups, J. Comb. Theory, Ser. B, Volume 14 (1973), pp. 61-86

[6] R.L. Graham; D.E. Knuth; O. Patashnik, Addison-Wesley Publishing Company, Reading, MA (1994), p. 1

[7] Y.L. Luke The Special Functions and Their Approximations, vol. I, Academic Press, New York, London, 1969

[8] M. Merca A note on the r-Whitney numbers of Dowling lattices, C. R. Acad. Sci. Paris, Ser. I, Volume 351 (2013), pp. 649-655

[9] I. Mezõ A new formula for the Bernoulli polynomials, Results Math., Volume 58 (2010), pp. 329-335

[10] M. Mihoubi; M. Tiachachat The values of the high order Bernoulli polynomials at integers and the r-Stirling numbers, 23 Jan. 2014 | arXiv

[11] G. Nemes An asymptotic expansion for the Bernoulli numbers of the second kind, J. Integer Seq., Volume 14 (2011) (article 11.4.8)

[12] T.R. Prabhakar; S. Gupta Bernoulli polynomials of the second kind and general order, Indian J. Pure Appl. Math., Volume 11 (1980), pp. 1361-1368

[13] M. Rahmani Some results on Whitney numbers of Dowling lattices, Arab J. Math. Sci., Volume 20 (2014) no. 1, pp. 11-27

[14] S. Roman The Umbral Calculus, Academic Press, 1984

[15] H.M. Srivastava An explicit formula for the generalized Bernoulli polynomials, J. Math. Anal. Appl., Volume 130 (1988), pp. 509-513

Cité par Sources :

Commentaires - Politique