Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions

Abstract

We have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions. Later, the generating functions and Binet formulas are obtained for Pauli Gaussian Fibonacci and Pauli Gaussian Lucas quaternions. Furthermore, Honsberger’s identity, Catalan’s and Cassini’s identities have been given for Pauli Gaussian Fibonacci quaternions.

Keywords

• Pauli matrix
• Pauli quaternion
• Fibonacci quaternion
• Pauli Gaussian Fibonacci quaternion
• Pauli Gaussian Lucas quaternion