One-parameter generalization of dual-hyperbolic Jacobsthal numbers
Abstract
In this paper, we introduce one-parameter generalization of dualhyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover, we give the generating function and summation formula for these numbers. The presented results are a generalization of the results for the dual-hyperbolic Jacobsthal numbers.
Keywords
Jacobsthal numbers; dual-hyperbolic numbers; dual-hyperbolic Jacobsthal numbers; Binet formula; Catalan identity; Cassini identity
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Wydział Matematyki i Fizyki Stosowanej, Politechnika Rzeszowska im. Ignacego Łukasiewicza Poland
https://orcid.org/0000-0001-5181-1725
Wydział Matematyki i Fizyki Stosowanej, Politechnika Rzeszowska im. Ignacego Łukasiewicza Poland
Wydział Matematyki i Fizyki Stosowanej, Politechnika Rzeszowska im. Ignacego Łukasiewicza Poland
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