Harmonic number identities via polynomials with r-Lah coefficients

Levent Kargın; Mümün Can

doi:10.5802/crmath.53

Théorie des nombres

Harmonic number identities via polynomials with r-Lah coefficients
[Identités sur les nombres harmonique via des polynômes à coefficients r-Lah]

Levent Kargın ¹ ; Mümün Can ¹

¹ Department of Mathematics, Akdeniz University, Antalya, Turkey

Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 535-550.

Résumé
Abstract

Dans cet article, des polynômes à coefficients faisant intervenir les nombres $r$ -Lah sont utilisés pour établir plusieurs formules de sommation en fonction des coefficients binomiaux, des nombres de Stirling et des nombres harmoniques ou hyper-harmoniques. De plus, nous introduisons le nombre asymétrique-hyper-harmonique et nous étudions ses propriétés de base.

In this paper, polynomials whose coefficients involve $r$ -Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers. Moreover, skew-hyperharmonic number is introduced and its basic properties are investigated.

Reçu le : 2020-02-05
Révisé le : 2020-04-18
Accepté le : 2020-04-19
Publié le : 2020-09-14

DOI : 10.5802/crmath.53

Classification : 11B75, 11B68, 47E05, 11B73, 11B83

Affiliations des auteurs :

Levent Kargın ¹ ; Mümün Can ¹

¹ Department of Mathematics, Akdeniz University, Antalya, Turkey

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Levent Karg{\i}n and M\"um\"un Can},
     title = {Harmonic number identities via polynomials with {r-Lah} coefficients},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {535--550},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {5},
     year = {2020},
     doi = {10.5802/crmath.53},
     language = {en},
}

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Levent Kargın; Mümün Can. Harmonic number identities via polynomials with r-Lah coefficients. Comptes Rendus. Mathématique, Volume 358 (2020) no. 5, pp. 535-550. doi : 10.5802/crmath.53. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.53/

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