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/lp/de-gruyter/on-a-new-one-parameter-generalization-of-dual-complex-jacobsthal-wJKc5othum
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- Publisher
- de Gruyter
- Copyright
- © 2021 Dorota Bród et al., published by Sciendo
- eISSN
- 2066-7752
- DOI
- 10.2478/ausm-2021-0007
- Publisher site
- See Article on Publisher Site
Abstract
AbstractIn this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal numbers - dual-complex r-Jacobsthal numbers. We investigate some algebraic properties of introduced numbers, among others Binet type formula, Catalan, Cassini, d’Ocagne and Honsberger type identities. Moreover, we present the generating function, summation formula and matrix generator for these numbers. The results are generalization of the properties for the dual-complex Jacobsthal numbers.
Journal
Acta Universitatis Sapientiae, Mathematica – de Gruyter
Published: Aug 1, 2021
Keywords: Jacobsthal numbers; dual-complex numbers; dual-complex Jacobsthal numbers; Binet formula; Catalan identity; Cassini identity; 11B37; 11B39