On hyperbolic lucas quaternions

Abstract

Many quaternions such as Fibonacci, Lucas, Pell and Jacob-sthal quaternions have been investigated in different forms before. Moreover, their fundamental identities have been presented. In this paper, we introduce new classes of quaternions associated with the symmetrical hyperbolic Lucas functions. In addition, we present the Binet's formulas, certain generating matrix representations and generating functions of these quaternions. In particular, we derive Cassini's formulas and d'Ocagne's identities.