Third-order Jacobsthal $3$-Parameter Generalized Quaternions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908302502264832 |
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| author | Morales, Gamaliel |
| author_facet | Morales, Gamaliel |
| contents | The purpose of this article is to bring together the third-order Jacobsthal numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and examine a new type of quite big special numbers system, which is called third-order Jacobsthal 3-parameter generalized quaternions (shortly, third-order Jacobsthal 3PGQs). Further, we compute both some new equations and classical well-known equations such as: linear recurrence, Binet formulas, generating function, sum formulas, Cassini identity and d'Ocagne identity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_03646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Third-order Jacobsthal $3$-Parameter Generalized Quaternions Morales, Gamaliel Rings and Algebras 11B37, 11K31, 11R52, 11Y55 The purpose of this article is to bring together the third-order Jacobsthal numbers and 3-parameter generalized quaternions, which are a general form of the quaternion algebra according to 3-parameters. With this purpose, we introduce and examine a new type of quite big special numbers system, which is called third-order Jacobsthal 3-parameter generalized quaternions (shortly, third-order Jacobsthal 3PGQs). Further, we compute both some new equations and classical well-known equations such as: linear recurrence, Binet formulas, generating function, sum formulas, Cassini identity and d'Ocagne identity. |
| title | Third-order Jacobsthal $3$-Parameter Generalized Quaternions |
| topic | Rings and Algebras 11B37, 11K31, 11R52, 11Y55 |
| url | https://arxiv.org/abs/2504.03646 |