On a new two-parameter generalization of dual-hyperbolic Jacobsthal numbers

Dorota Bród, Anetta Szynal-Liana, Iwona Włoch

Abstract


In this paper we introduce two-parameter generalization of dualhyperbolic Jacobsthal numbers: dual-hyperbolic (s,p)-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, d’Ocagne identities. Moreover, we give the generating function, matrix generator and summation formula for these numbers.

Keywords


Jacobsthal numbers; dual-hyperbolic numbers; dualhyperbolic Jacobsthal numbers; Binet formula; Catalan identity; Cassini identity

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References


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DOI: http://dx.doi.org/10.17951/a.2021.75.1.1-14
Date of publication: 2021-07-24 12:06:58
Date of submission: 2021-07-21 19:06:45


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