<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In 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.</p>
</abstract>

In 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.

On a new one-parameter generalization of dual-complex Jacobsthal numbers

The Faculty of Mathematics and Applied Physics

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On a new one-parameter generalization of dual-complex Jacobsthal numbers"}

In this paper we define dual-complex numbers with generalized Jacobsthal coefficients. We introduce one-parameter generalization of dual-complex Jacobsthal...

On a new one-parameter generalization of dual-complex Jacobsthal numbers

Published Online: Aug 26, 2021

Page range: 127 - 144

Received: Dec 21, 2020

DOI: https://doi.org/10.2478/ausm-2021-0007

Keywords
Jacobsthal numbers, dual-complex numbers, dual-complex Jacobsthal numbers, Binet formula, Catalan identity, Cassini identity

© 2021 Dorota Bród et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On a new one-parameter generalization of dual-complex Jacobsthal numbers

Published Online: Aug 26, 2021

Page range: 127 - 144

Received: Dec 21, 2020

DOI: https://doi.org/10.2478/ausm-2021-0007

KeywordsJacobsthal numbers, dual-complex numbers, dual-complex Jacobsthal numbers, Binet formula, Catalan identity, Cassini identity

© 2021 Dorota Bród et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Jacobsthal numbers, dual-complex numbers, dual-complex Jacobsthal numbers, Binet formula, Catalan identity, Cassini identity