On Recursive Hyperbolic Fibonacci Quaternions

Abstract

Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers. This article presents new classes of quaternions whose components are composed of symmetrical hyperbolic Fibonacci functions. In addition, the Binet's formulas, certain generating matrices, generating functions, Cassini's and d'Ocagne's identities for these quaternions are given.

Keywords

• binet
• cassini
• generating matrix
• hyperbolic fibonacci functions
• quaternion