Geodesic
On Balancing and Lucas-balancing Quaternions
Communications in Mathematics, Tome 29 (2021) no. 3, pp. 325-341.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

The 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.
Classification : 11B37, 11B39, 20G20
Keywords: Recurrence relations; Balancing numbers; Lucas-balancing numbers; Quaternions 
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Patel, Bijan Kumar; Ray, Prasanta Kumar. On Balancing and Lucas-balancing Quaternions. Communications in Mathematics, Tome 29 (2021) no. 3, pp. 325-341. http://geodesic.mathdoc.fr/item/COMIM_2021__29_3_a0/