On Unrestricted Horadam Generalized Quaternions

Abstract

We study on unrestricted Horadam generalized quaternions over the algebra H(A,/i) where A and/i are real numbers. We give generating function, Binet formula and generalizations of some well-known identities including Vajda's, Catalan's, Cassini's and d'Ocagne's identities. Also, we give some addition formulas for the unrestricted Horadam generalized quaternions.