Generalized Tribonacci Hyperbolic Spinors

TL;DR

This paper introduces generalized Tribonacci hyperbolic spinors, exploring their properties, relations with generalized Tribonacci numbers, and potential applications in mathematics and physics, including new formulas, algorithms, and future research directions.

Contribution

It presents the first comprehensive study of generalized Tribonacci hyperbolic spinors, establishing their properties and connections with generalized Tribonacci numbers and split quaternions.

Findings

Derived recurrence relations and formulas for generalized Tribonacci hyperbolic spinors.

Established relations between hyperbolic spinors and generalized Tribonacci numbers.

Developed numerical algorithms and identified future research directions.

Abstract

In this study, we introduce the generalized Tribonacci hyperbolic spinors and properties of this new special numbers system by the generalized Tribonacci numbers, which are one of the most general form of the third-order recurrence sequences, generalized Tribonacci quaternions, and hyperbolic spinors, which have quite an importance and framework from mathematics to physics. This study especially improves the relations between the hyperbolic spinors and generalized Tribonacci numbers with the help of the generalized Tribonacci split quaternions. Furthermore, we examine some special cases of them and construct both new equalities and fundamental properties such as recurrence relation, Binet formula, generating function, exponential generating function, Poisson generating function, summation formulas, special determinant properties, matrix formula, and special determinant equations. Also, we give some numerical algorithms with respect to the obtained materials. In addition to these, we give a brief introduction for further research: generalized Tribonacci polynomial hyperbolic spinor sequence.