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

<p>In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic <italic>r</italic>-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.</p>
</abstract>

In this paper, we introduce one-parameter generalization of dual-hyperbolic 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.

One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers

Annales Mathematicae Silesianae

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

{"article-title":"One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers"}

In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some...

One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers

Published Online: Apr 02, 2023

Page range: 224 - 239

Received: Dec 15, 2021

Accepted: Mar 06, 2023

DOI: https://doi.org/10.2478/amsil-2023-0005

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

© 2023 Dorota Bród et al., published by Sciendo

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

One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers

Published Online: Apr 02, 2023

Page range: 224 - 239

Received: Dec 15, 2021

Accepted: Mar 06, 2023

DOI: https://doi.org/10.2478/amsil-2023-0005

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

© 2023 Dorota Bród et al., published by Sciendo

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

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