Hyperbolic Jacobsthal spinor sequences and their mathematical properties

In this study, novel Hyperbolic spinor sequences of Jacobsthal, Jacobsthal–Lucas and Jacobsthal polynomial, which have not been studied before, are defined by investigating the relationship between spinors, which are important mathematical objects used in physics and mathematics, and split Jacobsthal and split Jacobsthal–Lucas quaternions, which are extensions of the known Jacobsthal and Jacobsthal–Lucas numbers to quaternion algebra. The recurrence relations of sequences whose members are Hyperbolic Jacobsthal, Jacobsthal–Lucas and Jacobsthal polynomial spinors are described. Additionally, certain properties of these spinors are presented, such as the generator function and Binet formula, and some identities resulting from these spinors are obtained.