On the Leonardo quaternions sequence

Beites, Patrícia Damas; Catarino, Paula Maria Machado Cruz

http://hdl.handle.net/10400.6/19693

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Autores

Beites, Patrícia Damas

Catarino, Paula Maria Machado Cruz

Resumo(s)

In the present work, a new sequence of quaternions related to the Leonardo numbers – named the Leonardo quaternions sequence – is defined and studied. Binet’s formula and certain sum and binomial-sum identities, some of which derived from the mentioned formula, are established. Tagiuri-Vajda’s identity and, as consequences, Catalan’s identity, d’Ocagne’s identity and Cassini’s identity are presented. Furthermore, applying Catalan’s identity, and the connection between composition algebras and vector cross product algebras, Gelin-Cesàro’s identity is also stated and proved. Finally, the generating function, the exponential generating function and the Poisson generating function are deduced. In addition to the results on Leonardo quaternions, known results on Leonardo numbers and on Fibonacci quaternions are extended.

Palavras-chave

Leonardo numbers Leonardo quaternions Binet’s formula Generating function

URI

http://hdl.handle.net/10400.6/19693

Citação

Beites, P., & Catarino, P. M. M. C. (2024). On the Leonardo quaternions sequence. Hacettepe Journal of Mathematics and Statistics, 53(4), 1001-1023. https://doi.org/10.15672/hujms.1197693