Abstract
In this paper, we introduce the bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions. We give the Binet formulas and the generating functions for these quaternions. We obtain some well-known identities such as the Cassini, Catalan and D’ocagne’s identities. Additionally, we give summation formulas and the relationships between bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions.
Publisher
Canadian Center of Science and Education
Cited by
3 articles.
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1. Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers;Journal of Mathematics;2023-01-06
2. Generalized k-Order Fibonacci Hybrid Quaternions;Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi;2022-08-09
3. Dual bicomplex Horadam quaternions;Notes on Number Theory and Discrete Mathematics;2020-11