Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions
In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.
| Published in: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2015-06-01
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| Subjects: | |
| Online Access: | https://doi.org/10.1515/auom-2015-0037 |
| _version_ | 1857059801984401408 |
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| author | Ramírez José L. |
| author_facet | Ramírez José L. |
| author_sort | Ramírez José L. |
| collection | DOAJ |
| container_title | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| description | In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity. |
| format | Article |
| id | doaj-art-e554b9c6c0884ca8a449d74edb74b53e |
| institution | Directory of Open Access Journals |
| issn | 1844-0835 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Sciendo |
| record_format | Article |
| spelling | doaj-art-e554b9c6c0884ca8a449d74edb74b53e2025-08-19T19:29:37ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352015-06-0123220121210.1515/auom-2015-0037Some Combinatorial Properties of the k-Fibonacci and the k-Lucas QuaternionsRamírez José L.0Instituto de Matemáticas y sus Aplicaciones, Universidad Sergio Arboleda, Bogotá, ColombiaIn this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.https://doi.org/10.1515/auom-2015-0037k-fibonacci numbersk-lucas numbersquaternionsgenerating function |
| spellingShingle | Ramírez José L. Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions k-fibonacci numbers k-lucas numbers quaternions generating function |
| title | Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions |
| title_full | Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions |
| title_fullStr | Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions |
| title_full_unstemmed | Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions |
| title_short | Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions |
| title_sort | some combinatorial properties of the k fibonacci and the k lucas quaternions |
| topic | k-fibonacci numbers k-lucas numbers quaternions generating function |
| url | https://doi.org/10.1515/auom-2015-0037 |
| work_keys_str_mv | AT ramirezjosel somecombinatorialpropertiesofthekfibonacciandtheklucasquaternions |