Mersenne banner
no. 2
Sur une propriété des polynômes de Nörlund
Farid Bencherif1
1 USTHB, Fac. Math., P.B. 32, El Alia, 16111, Algiers, Algeria.
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 71-77.

In this paper, we prove a remarkable property of the coefficients of Nörlund’s polynomials obtained mainly from a result of J.-L. Chabert.

Published online:
DOI: 10.5802/acirm.36
Classification: 11B68, 11B83
Keywords: Bernoulli numbers
Farid Bencherif 1

1 USTHB, Fac. Math., P.B. 32, El Alia, 16111, Algiers, Algeria. 
@article{ACIRM_2010__2_2_71_0,
     author = {Farid Bencherif},
     title = {Sur une propri\'et\'e des polyn\^omes de {N\"orlund}},
     journal = {Actes des rencontres du CIRM},
     pages = {71--77},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.5802/acirm.36},
     zbl = {06938584},
     language = {fr},
     url = {https://pmb.cedram.org/articles/10.5802/acirm.36/}
}
TY  - JOUR
AU  - Farid Bencherif
TI  - Sur une propriété des polynômes de Nörlund
JO  - Actes des rencontres du CIRM
PY  - 2010
SP  - 71
EP  - 77
VL  - 2
IS  - 2
PB  - CIRM
UR  - https://pmb.cedram.org/articles/10.5802/acirm.36/
DO  - 10.5802/acirm.36
LA  - fr
ID  - ACIRM_2010__2_2_71_0
ER  - 
%0 Journal Article
%A Farid Bencherif
%T Sur une propriété des polynômes de Nörlund
%J Actes des rencontres du CIRM
%D 2010
%P 71-77
%V 2
%N 2
%I CIRM
%U https://pmb.cedram.org/articles/10.5802/acirm.36/
%R 10.5802/acirm.36
%G fr
%F ACIRM_2010__2_2_71_0
Farid Bencherif. Sur une propriété des polynômes de Nörlund. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 71-77. doi : 10.5802/acirm.36. https://pmb.cedram.org/articles/10.5802/acirm.36/

[1] A. Adelberg, Arithmetic properties of the Nörlund polynomial B n (x) , Discrete Mathematics, (H. W. Gould volume) 204 (1999), 5-13. | DOI | Zbl

[2] F. Bencherif et T. Garici, Sur une propriété des polynômes de Stirling, Preprint (soumis).

[3] F. Bencherif et A. Zekiri, On some properties of Nörlund’s polynomials, Preprint.

[4] L. Carlitz, Note on the Nörlund polynomial B n (x) , Proc. Amer. Math. Soc. 11 (1960), 452-455. | DOI | Zbl

[5] L. Carlitz, Some properties of the Norlund polynomial B n (x) , Math. Nachr. 33 (1967), 297-311. | DOI | Zbl

[6] J.-L. Chabert, Integer-valued polynomials on prime numbers and logarithm power expansion, European Journal of Combinatorics 28 (2007), 754-761. | DOI | MR | Zbl

[7] J.-L. Chabert and P.-J. Cahen, Old Problems and New Questions around Integer-Valued Polynomials and Factorial Sequences, in Multiplicative Ideal Theory in Commutative Algebra, Springer, 2006, 89-108. | DOI | Zbl

[8] L. Comtet Analyse Combinatoire, Presses Universitaires de France, Paris, Vol. 1 & 2, 1970. | DOI

[9] I. M. Gessel, On Miki’s identity for Bernoulli numbers, J. Number Theory 110 (2005),75-82. | DOI | MR | Zbl

[10] H. W. Gould, The Lagrange interpolation formula and Stirling numbers, Proc. Amer. Math. Soc. 11 (1960), 421-425. | DOI | MR | Zbl

[11] R.L. Graham, D.E. Knuth, and O. Patashnick, Concrete Mathematics : a Foundation for Computer Science, Addison-Wesley, 1994. | Zbl

[12] R.M. Guralnick and M. Lorentz, Orders of Finite Groups of Matrices, arXiv :math/0511191v1 [math.GR] v1] 8 Nov 2005. | DOI

[13] G.-D. Liu and H. M. Srivastava, Explicit Formulas for the Nörlund Polynomials B n (x) and b n (x) , Computers & Mathematics with Applications Vol. 51, n ∘ 9-10, (2006), 1377-1384. | DOI | Zbl

[14] D.S. Mitrinović et R.S. Mitrinović, Tableaux qui fournissent des polynômes de Stirling, Publications de la Faculté d’Electronique, série : Mathématiques et physique, N ∘ 34, (1960) 1-23. | Zbl

[15] D.S. Mitrinović, Sur une relation de récurrence relative aux nombres de Bernoulli d’ordre supérieur, C. R. Acad. Sc. Paris 250 (1960), 4266-4267. | Zbl

[16] N.E. Nörlund, Vorlesungen über Differenzenrechnung, Springer, Berlin, 1924 ; repr. Chelsea Publ. Comp., New York, 1954. | DOI | Zbl

[17] N.J.A. Sloane, The On-Line Encylopedia of Integer Sequences, http ://www.research.att.com/~njas/sequences/ index.htm. | DOI

Cited by Sources: