Third-order Jacobsthal $3$-Parameter Generalized Quaternions

Gamaliel Morales

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arXiv · 2504.03646

Third-order Jacobsthal $3$-Parameter Generalized Quaternions

Gamaliel Morales

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Abstract

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.

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Gamaliel Morales. 2025-02-12. Third-order Jacobsthal $3$-Parameter Generalized Quaternions. https://arxiv.org/abs/2504.03646

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