Comptes Rendus
Combinatoire, Physique mathématique
A two-sided Faulhaber-like formula involving Bernoulli polynomials
[Une formule bilatérale de type Faulhaber utilisant les polynômes de Bernoulli]
Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 41-44.

Nous donnons une nouvelle identité utilisant les polynômes de Bernoulli et les coefficient binomiaux. Ceci fournit, en particulier, une formule de type Faulhaber pour des sommes de la forme 1 m (n-1) m +2 m (n-2) m ++(n-1) m 1 m m et n sont des entiers positifs.

We give a new identity involving Bernoulli polynomials and combinatorial numbers. This provides, in particular, a Faulhaber-like formula for sums of the form 1 m (n-1) m +2 m (n-2) m ++(n-1) m 1 m for positive integers m and n.

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Révisé le :
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Publié le :
DOI : 10.5802/crmath.10

J. Fernando Barbero G. 1, 2 ; Juan Margalef-Bentabol 1, 3, 4 ; Eduardo J.S. Villaseñor 5, 1

1 Grupo de Teorías de Campos y Física Estadística. Instituto Gregorio Millán (UC3M). Unidad Asociada al Instituto de Estructura de la Materia, CSIC, Madrid, Spain
2 Instituto de Estructura de la Materia, CSIC. Serrano 123, 28006 Madrid, Spain
3 Institute for Gravitation and the Cosmos & Physics Department, Penn State, University Park, PA 16802, USA
4 Laboratory of Geometry and Dynamical Systems, Department of Mathematics, EPSEB, Universitat Politècnica de Catalunya, BGSMath, Barcelona, Spain
5 Departamento de Matemáticas, Universidad Carlos III de Madrid. Avda. de la Universidad 30, 28911 Leganés, Spain
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     author = {J. Fernando Barbero G. and Juan Margalef-Bentabol and Eduardo J.S. Villase\~nor},
     title = {A two-sided {Faulhaber-like} formula involving {Bernoulli} polynomials},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {41--44},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     year = {2020},
     doi = {10.5802/crmath.10},
     language = {en},
}
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%A Eduardo J.S. Villaseñor
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J. Fernando Barbero G.; Juan Margalef-Bentabol; Eduardo J.S. Villaseñor. A two-sided Faulhaber-like formula involving Bernoulli polynomials. Comptes Rendus. Mathématique, Volume 358 (2020) no. 1, pp. 41-44. doi : 10.5802/crmath.10. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.10/

[1] J. Fernando Barbero G.; Juan Margalef-Bentabol; Eduardo J. S. Villaseñor On the distribution of the eigenvalues of the area operator in loop quantum gravity, Class. Quant. Grav., Volume 35 (2018) no. 6, 065008, 17 pages | MR | Zbl

[2] Petro Kolosov On the relation between binomial theorem and discrete convolution of piecewise defined power function (2016) (https://arxiv.org/abs/1603.02468)

[3] N. J. A. Sloane The On-Line Encyclopedia of Integer Sequences, 2010 (http://oeis.org)

[4] Zhi-Wei Sun Combinatorial identities in dual sequences, Eur. J. Comb., Volume 24 (2003) no. 6, pp. 709-718 | MR | Zbl

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