Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

On The Generalized Leonardo Quaternions and Associated Spinors

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Authors: M. KUMARI, K. PRASAD, H. MAHATO AND P. M. M. C. CATARINO

DOI: 10.46793/KgJMat2603.425K

Abstract:

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.

Keywords:

Leonardo number, generalized Leonardo quaternions, generalized Leonardo spinors, Binet’s formula, generating function, series sum.

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