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Harmonic number identities via polynomials with r-Lah coefficients

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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… Click to show full abstract

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. Résumé. 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 asymétriquehyper-harmonique et nous étudions ses propriétés de base. 2020 Mathematics Subject Classification. 11B75, 11B68, 47E05, 11B73, 11B83. Manuscript received 5th February 2020, revised 18th April 2020, accepted 19th April 2020.

Keywords: number; number identities; harmonic number; via polynomials; identities via; polynomials lah

Journal Title: Comptes Rendus Mathematique
Year Published: 2020

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