Pauli–Leonardo quaternions

Abstract

In this study, we define Pauli–Leonardo quaternions by taking the coefficients of the Pauli quaternions as Leonardo numbers. We give the recurrence relation, Binet formula, generating function, exponential generating function, some special equalities, and the sum properties of these novel quaternions. In addition, we investigate the interrelations between Pauli–Leonardo quaternions and the Pauli–Fibonacci, Pauli–Lucas quaternions. Moreover, we create some algorithms that determine the terms of the Pauli–Leonardo quaternions. Finally, we generate the matrix representations of the Pauli–Leonardo quaternions and ℝ-linear transformations.