Third-order Jacobsthal $3$-Parameter Generalized Quaternions
Rings and Algebras
2025-04-08 v1
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.
Cite
@article{arxiv.2504.03646,
title = {Third-order Jacobsthal $3$-Parameter Generalized Quaternions},
author = {Gamaliel Morales},
journal= {arXiv preprint arXiv:2504.03646},
year = {2025}
}