2025/02/12 by Morales, Gamaliel
#11B37 #11K31 #11R52 #11Y55 #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2504.03646
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.