In this paper we generalize Jacobsthal quaternions to Jacobsthal quaternions. We give some of their properties, among others the Binet formula, the generating function and the matrix representation of these quaternions. We will show how a graph interpretation can be used in proving some identities for quaternions.
In this paper we introduce the Pell and Pell−Lucas hybrid numbers as special kinds of hybrid numbers. We describe some properties of Pell hybrid numbers and Pell−Lucas hybrid numbers among other we give the Binet formula, the character and the generating function for these numbers.
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions.
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