• Corpus ID: 238857062

On the sum of the values of a polynomial at natural numbers which form a decreasing arithmetic progression

@inproceedings{Farhi2021OnTS,
  title={On the sum of the values of a polynomial at natural numbers which form a decreasing arithmetic progression},
  author={Bakir Farhi},
  year={2021}
}
The purpose of this paper consists to study the sums of the type P (n) + P (n − d) + P (n − 2d) + . . . , where P is a real polynomial, d is a positive integer and the sum stops at the value of P at the smallest natural number of the form (n − kd) (k ∈ N). Precisely, for a given d, we characterize the R-vector space Ed constituting of the real polynomials P for which the above sum is polynomial in n. The case d = 2 is studied in more details. In the last part of the paper, we approach the… 

References

SHOWING 1-8 OF 8 REFERENCES
A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials.
This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related
Arithmetic properties of the Genocchi numbers and their generalization
This note is devoted to establish some new arithmetic properties of the generalized Genocchi numbers Gn,a (n ∈ N, a ≥ 2). The resulting properties for the usual Genocchi numbers Gn = Gn,2 are then
Advanced Combinatorics: The Art of Finite and Infinite Expansions
I. Vocabulary of Combinatorial Analysis.- 1.1. Subsets of a Set Operations.- 1.2. Product Sets.- 1.3. Maps.- 1.4. Arrangements, Permutations.- 1.5. Combinations (without repetitions) or Blocks.- 1.6.
"Raf al-hijab" d'Ibn al-Banna : édition critique, traduction, étude philosophique et analyse mathématique
Ce travail consacre essentiellement a l'edition critique et a la traduction francaise du Raf al-hijab d'Ibn al-Banna al-Murrakushi (m. 1321), a ete complete par une introduction qui contient en
Enumerative combinatorics, vol. 1, 2 edition, Cambridge Studies in Advanced Mathematics 49
  • 2011
Traité Élémentaire des nombres de bernoulli
Intorno all espressioni generali di numeri Bernoulliani
  • Annali di scienze mat. e fisiche, compilati da Barnaba Tortolini,
  • 1852
Ars Conjectandi