On the Generalized k-Horadam-Like Sequences

Prasad, Kalika; Mahato, Hrishikesh; Kumari, Munesh

doi:10.1007/978-3-031-19082-7_2

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2024

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“…İşbilir et al [23] investigated the Pauli-Leonardo quaternions. Some recent developments on Leonardo numbers, their generalizations and interesting properties can be seen in [3,5,[14][15][16][17][18][19]22]. Here we restate some of them.…”

Section: Introductionmentioning

confidence: 99%

On The Generalized Leonardo Quaternions and Associated Spinors

KUMARI,

PRASAD,

MAHATO

et al. 2024

KgJMat

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In this paper, we introduce and study a new family of sequences called the generalized Leonardo spinors by deﬁning a linear correspondence between the generalized Leonardo quaternions and spinors. We start with deﬁning the generalized Leonardo quaternions and then present their some important properties such as Binet type formula, Catalan’s identity, d’Ocagne’s identity, series sums, etc. We give some interrelations of these quaternions with the Fibonacci and Lucas quaternions. Then, we present the generating functions, sum formulae, various well-known identities, etc. for the Leonardo spinors and show their connection with the Fibonacci and Lucas spinors.

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