Hyperbolic Jacobsthal Spinor Sequences and Their Mathematical Properties

TL;DR

This paper introduces new hyperbolic Jacobsthal spinor sequences, explores their mathematical properties, and establishes their recurrence relations, generating functions, Binet formulas, and identities, extending the understanding of spinors in quaternion algebra.

Contribution

It defines and analyzes novel hyperbolic Jacobsthal spinor sequences and their properties, which have not been studied before, linking spinors with split Jacobsthal quaternions.

Findings

Recurrence relations for hyperbolic Jacobsthal spinors

Derivation of generating functions and Binet formulas

New identities involving these spinors

Abstract

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, such as the generator function and Binet formula, are presented and some identities resulting from these spinors are obtained.