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Keywords:
Recurrence relations; Balancing numbers; Lucas-balancing numbers; Quaternions
Recurrence relations; Balancing numbers; Lucas-balancing numbers; Quaternions
Summary:
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.
References:
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