Hyperbolic (s,t)-Fibonacci and (s,t)-Lucas Quaternions

Abstract

In this study, we define hyperbolic (s,t)-Fibonacci and (s,t)-Lucas quaternions. For these hyperbolic quaternions, we give the special summation formulas, special generating functions, etc. Also, we calculate the special identities of these hyperbolic quaternions. In addition, we obtain the Binet formulas in two different ways. The first is in the known classical way and the second is with the help of the sequence's generating functions. Moreover, we examine the relationships between the hyperbolic (s,t)-Fibonacci and (s,t)-Lucas quaternions. Finally, the terms of the (s,t)-Fibonacci and (s,t)-Lucas sequences are associated with their hyperbolic quaternion values.