Pure and Applied Mathematics Quarterly

Volume 14 (2018)

Number 3-4

On $J(r,n)$-Jacobsthal quaternions

Pages: 579 – 590

DOI: https://dx.doi.org/10.4310/PAMQ.2018.v14.n3.a7

Authors

Dorota Bród (Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Rzeszów, Poland)

Anetta Szynal-Liana (Faculty of Mathematics and Applied Physics, Rzeszow University of Technology, Rzeszów, Poland)

Abstract

In this paper we introduce the $J(r, n)$-Jacobsthal quaternions and give some of their properties, among others the Binet formula, convolution identity and the generating function.

Keywords

Jacobsthal numbers, quaternions, recurrence relations

2010 Mathematics Subject Classification

Primary 11B37. Secondary 11R52.

Received 17 April 2019

Accepted 6 August 2019

Published 5 November 2019