Hyperbolic k-Oresme and k-Oresme-Lucas Quaternions

In this study, we define hyperbolic k-Oresme and k-Oresme-Lucas quaternions. For these quaternions, we give the Binet Formulas, summation formulas, etc. Then we obtain the generating functions and exponential generating functions of these quaternions. Also, we find relations among the hyperbolic k- Oresme and k-Oresme-Lucas quaternions and their conjugates. In addition, we calculate the special identities of these quaternions. Moreover, we examine the relationships between the hyperbolic k-Oresme and k-Oresme-Lucas quaternions. Finally, the terms of the k-Oresme and k-Oresme-Lucas sequences are associated with their hyperbolic quaternion values.In this study, we define hyperbolic k-Oresme and k-Oresme-Lucas quaternions. For these quaternions, we give the Binet Formulas, summation formulas, etc. Then we obtain the generating functions and exponential generating functions of these quaternions. Also, we find relations among the hyperbolic k-Oresme and k-Oresme-Lucas quaternions and their conjugates. In addition, we calculate the special identities of these quaternions. Moreover, we examine the relationships between the hyperbolic k-Oresme and k-Oresme-Lucas quaternions. Finally, the terms of the k-Oresme and k-Oresme-Lucas sequences are associated with their hyperbolic quaternion values.