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Sur une propriété des polynômes de Nörlund
Farid Bencherif
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, p. 71-77
  • 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.

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Published online : 2011-10-20
DOI : https://doi.org/10.5802/acirm.36
Classification:  11B68,  11B83
@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},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     pages = {71-77},
     doi = {10.5802/acirm.36},
     language = {fr},
     url = {https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_71_0}
}
Bencherif, Farid. 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://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_71_0/
  • References

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[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.

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

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

[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.

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

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

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

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

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

[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.

[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.

[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.

[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.

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