On Third Order Bronze Fibonacci Quaternions

Abstract

In this study, we define third order bronze Fibonacci quaternions. We obtain the generating functions, the Binet's formula and some properties of these quaternions. We give d'Ocagne's-like and Cassini's-like identity and we use q-determinants for quaternionic matrices to give the Cassini's identity for third order bronze Fibonacci quaternions.

Keywords

• Bronze Fibonacci quaternions
• generating function
• Binet's formula
• Cassini's identity

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