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On Balancing and Lucas-balancing Quaternions

On Balancing and Lucas-balancing Quaternions AbstractThe aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet’s formulas, summation formulas, Catalan’s identity, etc. concerning these quaternions are also established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematics de Gruyter

On Balancing and Lucas-balancing Quaternions

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Publisher
de Gruyter
Copyright
© 2021 Bijan Kumar Patel et al., published by Sciendo
eISSN
2336-1298
DOI
10.2478/cm-2021-0010
Publisher site
See Article on Publisher Site

Abstract

AbstractThe aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet’s formulas, summation formulas, Catalan’s identity, etc. concerning these quaternions are also established.

Journal

Communications in Mathematicsde Gruyter

Published: Dec 1, 2021

Keywords: Recurrence relations; Balancing numbers; Lucas-balancing numbers; Quaternions; 11B37; 11B39; 20G20

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