Sur une propriété des polynômes de Nörlund

Farid Bencherif[1]

  • [1] USTHB, Fac. Math., P.B. 32, El Alia, 16111, Algiers, Algeria.

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 71-77
  • ISSN: 2105-0597

Abstract

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

How to cite

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Bencherif, Farid. "Sur une propriété des polynômes de Nörlund." Actes des rencontres du CIRM 2.2 (2010): 71-77. <http://eudml.org/doc/196275>.

@article{Bencherif2010,
abstract = {In this paper, we prove a remarkable property of the coefficients of Nörlund’s polynomials obtained mainly from a result of J.-L. Chabert.},
affiliation = {USTHB, Fac. Math., P.B. 32, El Alia, 16111, Algiers, Algeria.},
author = {Bencherif, Farid},
journal = {Actes des rencontres du CIRM},
keywords = {Bernoulli numbers},
language = {fre},
number = {2},
pages = {71-77},
publisher = {CIRM},
title = {Sur une propriété des polynômes de Nörlund},
url = {http://eudml.org/doc/196275},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Bencherif, Farid
TI - Sur une propriété des polynômes de Nörlund
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 71
EP - 77
AB - In this paper, we prove a remarkable property of the coefficients of Nörlund’s polynomials obtained mainly from a result of J.-L. Chabert.
LA - fre
KW - Bernoulli numbers
UR - http://eudml.org/doc/196275
ER -

References

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  1. A. Adelberg, Arithmetic properties of the Nörlund polynomial B n ( x ) , Discrete Mathematics, (H. W. Gould volume) 204 (1999), 5-13. Zbl0940.11011MR1691859
  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. Zbl0100.01705MR114768
  5. L. Carlitz, Some properties of the Norlund polynomial B n ( x ) , Math. Nachr.33 (1967), 297-311. Zbl0154.29301MR217034
  6. J.-L. Chabert, Integer-valued polynomials on prime numbers and logarithm power expansion, European Journal of Combinatorics28 (2007), 754-761. Zbl1120.11016MR2300756
  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. Zbl1117.13022MR2265803
  8. L. Comtet Analyse Combinatoire, Presses Universitaires de France, Paris, Vol. 1 & 2, 1970. Zbl0221.05002MR262087
  9. I. M. Gessel, On Miki’s identity for Bernoulli numbers, J. Number Theory110 (2005),75-82. Zbl1073.11013MR2114674
  10. H. W. Gould, The Lagrange interpolation formula and Stirling numbers, Proc. Amer. Math. Soc.11 (1960), 421-425. Zbl0102.04904MR114769
  11. R.L. Graham, D.E. Knuth, and O. Patashnick, Concrete Mathematics : a Foundation for Computer Science, Addison-Wesley, 1994. Zbl0668.00003MR1397498
  12. R.M. Guralnick and M. Lorentz, Orders of Finite Groups of Matrices, arXiv :math/0511191v1 [math.GR] v1] 8 Nov 2005. Zbl1203.20042MR2279238
  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. Zbl1161.11314MR2237635
  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. Zbl0146.24902
  15. D.S. Mitrinović, Sur une relation de récurrence relative aux nombres de Bernoulli d’ordre supérieur, C. R. Acad. Sc. Paris250 (1960), 4266-4267. Zbl0099.28102MR121307
  16. N.E. Nörlund, Vorlesungen über Differenzenrechnung, Springer, Berlin, 1924 ; repr. Chelsea Publ. Comp., New York, 1954. 
  17. N.J.A. Sloane, The On-Line Encylopedia of Integer Sequences, http ://www.research.att.com/~njas/sequences/ index.htm. Zbl1274.11001

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