On split r-Jacobsthal quaternions

Dorota Bród

Abstract


In this paper we introduce a one-parameter generalization of the split Jacobsthal quaternions, namely the split r-Jacobsthal quaternions. We give a generating function, Binet formula for these numbers. Moreover, we obtain some identities, among others Catalan, Cassini identities and convolution identity for the split r-Jacobsthal quaternions.

Keywords


Jacobsthal numbers; quaternion; split quaternion; split Jacobsthal quaternion; Binet formula

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References


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DOI: http://dx.doi.org/10.17951/a.2020.74.1.1-14
Date of publication: 2020-10-20 20:07:58
Date of submission: 2020-10-10 21:21:01


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