On Tribonacci and Tribonacci-Lucas Quaternion Polynomials

TL;DR

This paper introduces Tribonacci and Tribonacci-Lucas quaternion polynomials, deriving formulas, generating functions, and properties to expand the mathematical understanding of these quaternion sequences.

Contribution

It presents the first definitions and key formulas for Tribonacci and Tribonacci-Lucas quaternion polynomials, including Binet and generating functions.

Findings

Derived Binet formulas for the quaternion polynomials

Established generating and exponential generating functions

Presented properties and identities of the quaternion sequences

Abstract

In this paper, we introduce the Tribonacci and Tribonacci-Lucas quaternion polynomials. We obtain the Binet formulas, generating functions and exponential generating functions of these quaternions. Moreover, we give some properties and identities for the Tribonacci and Tribonacci-Lucas quaternions.