ON FIBONACCI AND LUCAS ELLIPTIC QUATERNIONS

This paper presents a novel class of quaternions derived from the concept of elliptic quaternions. Specifically, we establish the Fibonacci and Lucas elliptic quaternions, serving as a natural extension of the Fibonacci and Lucas quaternions. Our study delves into the fundamental properties of these sequences, including recurrence relations, generating functions, Binet-like formulas, and Vajda’s identity. We additionally establish relations involving both Fibonacci and Lucas elliptic quaternions.