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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.37 no.4 Antofagasta dic. 2018

http://dx.doi.org/10.4067/S0716-09172018000400731 

Articles

Dual third-order Jacobsthal quaternions

Gamaliel Cerda-Morales1 

1 Pontificia Universidad Católica de Valparaíso, Instituto de Matemáticas, Blanco Viel 596, Valparaíso, Chile, e-mail: gamaliel.cerda.m@mail.pucv

Abstract

In 2016, Yüce and Torunbalcı Aydın (18) defined dual Fibonacci quaternions. In this paper, we defined the dual third-order Jacobsthal quaternions and dual third-order Jacobsthal-Lucas quaternions. Also, we investigated the relations between the dual third-order Jacobsthal quaternions and third-order Jacobsthal numbers. Furthermore, we gave some their quadratic properties, the summations, the Binet’s formulas and Cassini-like identities for these quaternions.

Key words: Third-order Jacobsthal number; third-order Jacobsthal-Lucas number; third-order Jacobsthal quaternions; third-order Jacobsthal-Lucas quaternions; dual quaternion

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgments

The author would like to thank the anonymous referee for helpful comments on the original manuscript.

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Received: February 2018; Accepted: April 2018

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