Pauli Gaussian Leonardo quaternions

Abstract

In this paper, a new family of Pauli quaternions whose components are the Gaussian Leonardo numbers is defined. These new Pauli quaternions are called Pauli Gaussian Leonardo quaternions. Furthermore, several properties of Pauli Gaussian Leonardo quaternions, including relations with the Pauli Gaussian Fibonacci and Pauli Gaussian Lucas quaternions are investigated. In addition, Binet-like formula, (ordinary) generating function, exponential generating function, and some summation formulas for these Pauli quaternions are given. Moreover, some results are illustrated with examples.