<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

Data publikacji: 02 kwi 2023

Zakres stron: 224 - 239

Otrzymano: 15 gru 2021

Przyjęty: 06 mar 2023

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

Słowa kluczowe
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

Data publikacji: 02 kwi 2023

Zakres stron: 224 - 239

Otrzymano: 15 gru 2021

Przyjęty: 06 mar 2023

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

Słowa kluczoweJacobsthal 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.

Słowa kluczowe
Jacobsthal numbers, dual-hyperbolic numbers, dual-hyperbolic Jacobsthal numbers, Binet formula, Catalan identity, Cassini identity