Octonions and hyperbolic octonions with the \(k\)-balancing and \(k\)-Lucas balancing numbers

DOI10.1007/S41478-023-00716-XMaRDI QIDQ6649379

Munesh Kumari, Kalika Prasad, Jagmohan Tanti

Publication date: 5 December 2024

Published in: The Journal of Analysis (Search for Journal in Brave)

zbMATH Keywords

generating functionsCatalan's identityBinet's formula\(k\)-balancing hyperbolic octonions\(k\)-balancing octonions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Recurrences (11B37) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Cites Work

• On Pell quaternions and Pell-Lucas quaternions
• A note on Jacobsthal quaternions
• The modified Pell and the modified \(k\)-Pell quaternions and octonions
• Split Fibonacci and Lucas octonions
• Matrix representations of octonions and their applications
• Hyperbolic \(k\)-Jacobsthal and \(k\)-Jacobsthal-Lucas quaternions
• Identities concerning \(k\)-balancing and \(k\)-Lucas-balancing numbers of arithmetic indexes
• The Fibonacci octonions
• On balancing and Lucas-balancing quaternions
• Complex Fibonacci Numbers and Fibonacci Quaternions
• Hyperbolic \(k\)-Fibonacci and \(k\)-Lucas quaternions

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