Research Centre Didactics and Technology in the Education of Trainers

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Publication . Beites, Patrícia Damas ; Catarino, Paula Maria Machado Cruz

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.

2024-08-27Artigo científico

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Palavras-chave

Multiliteracies and Sustainability,Diversities and Curriculum,Professional and Human Development,Educational Policies, Quality and Evaluation,

Entidade financiadora

Fundação para a Ciência e a Tecnologia, I.P.

Programa de financiamento

Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Programático

Número da atribuição

UIDP/00194/2020