Generalized k-Order Fibonacci Hybrid Quaternions

In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, the matrix representation for generalized k-order Fibonacci hybrid quaternions is determined. The Q_k matrix defined for k-order Fibonacci numbers is given for the generalized k-order Fibonacci hybrid quaternions. By the means of this matrix and another defined matrices, several identities of these quaternions are also obtained.