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

<p>In this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of <italic>r</italic>-Pell numbers, we define the <italic>r</italic>-Pell hybrid numbers. We give their properties: character, Binet formula, summation formula, and generating function. Moreover, we present Catalan, Cassini, d’Ocagne, and Vajda type identities for the <italic>r</italic>-Pell hybrid numbers.</p>
</abstract>

In this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of r-Pell numbers, we define the r-Pell hybrid numbers. We give their properties: character, Binet formula, summation formula, and generating function. Moreover, we present Catalan, Cassini, d’Ocagne, and Vajda type identities for the r-Pell hybrid numbers.

On a New Generalization of Pell Hybrid Numbers

Annales Mathematicae Silesianae

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

{"article-title":"On a New Generalization of Pell Hybrid Numbers"}

In this paper, we define and study a new one-parameter generalization of the Pell hybrid numbers. Based on the definition of r-Pell numbers, we define the...

On a New Generalization of Pell Hybrid Numbers

Published Online: Apr 27, 2024

Page range: -

Received: Dec 10, 2022

Accepted: Mar 25, 2024

DOI: https://doi.org/10.2478/amsil-2024-0011

Keywords
recurrence relations, complex numbers, hyperbolic numbers, dual numbers, hybrid numbers, Pell hybrid numbers

© 2024 Dorota Bród et al., published by Sciendo

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

On a New Generalization of Pell Hybrid Numbers

Published Online: Apr 27, 2024

Page range: -

Received: Dec 10, 2022

Accepted: Mar 25, 2024

DOI: https://doi.org/10.2478/amsil-2024-0011

Keywordsrecurrence relations, complex numbers, hyperbolic numbers, dual numbers, hybrid numbers, Pell hybrid numbers

© 2024 Dorota Bród et al., published by Sciendo

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

Keywords
recurrence relations, complex numbers, hyperbolic numbers, dual numbers, hybrid numbers, Pell hybrid numbers