A Note on Hybrid Numbers with Generalized Hybrid k-Pell Numbers as Coefficients
In this study, we define a new generalization of the hybrid $k$-Pell sequence consisting of hybrid numbers with generalized hybrid $k$-Pell numbers as coefficients. We establish some algebraic properties and also the Binet formula, generating function, and exponential generating function related to this new sequence. In addition, some identities are provided as sum identities, and Catalan, Cassini, and d'Ocagne's identities. The particular cases are studied, namely, the hybrid numbers with hybrid $k$-Pell numbers as coefficients, the hybrid numbers with hybrid $k$-Pell--Lucas numbers as coefficients, and the hybrid numbers with hybrid Modified $k$-Pell numbers as coefficients.
Authors
- Paula Catarino (ORCID: https://orcid.org/0000-0001-6917-5093)
- Eudes Antônio Costa (ORCID: https://orcid.org/0000-0001-6684-9961)
- Elen Viviani Pereira Spreafico (ORCID: https://orcid.org/0000-0001-6079-2458)
Institutions
- Universidade Federal de Mato Grosso do Sul (BR)
- University of Trás-os-Montes and Alto Douro (PT)
- Universidade Federal do Tocantins (BR)
Publication Details
- Journal
- Communications in Advanced Mathematical Sciences
- Published
- 2025-07-18
- DOI
- https://doi.org/10.33434/cams.1655752
- Primary Topic
- Advanced Mathematical Theories and Applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministerio de Economía y Competitividad
- Universidade do Minho
- Universidade de Trás-os-Montes e Alto Douro
- Universidade Federal de Mato Grosso do Sul
- Fundação para a Ciência e a Tecnologia
- Pró-Reitoria de Pesquisa, Universidade Federal do Rio Grande do Sul