On the symmetrical second order hyperbolic quaternions sequences

Abstract

The purpose of this study is to obtain a new generalized quaternions sequences byusing hyperbolic functions with second order recurrence sequences. First of all, we define thesymmetrical second order hyperbolicsineand the symmetrical second order hyperboliccosinequaternions. Then, we investigate norms and some relations between these type of quaternions.We also obtain generating functions, Binet formulas, Catalan’s identity, Cassini’s identity andd’Ocagne’s identity of second order hyperbolic quaternions sequences