Some Properties of Horadam quaternions

TL;DR

This paper explores properties of Horadam quaternions, a generalized form of Fibonacci quaternions, using Binet's formula to derive identities and properties that extend classical Fibonacci number relations.

Contribution

It introduces generalized identities for Horadam quaternions and applies Binet's formula to analyze their properties, expanding the mathematical understanding of these sequences.

Findings

Derived new identities for Horadam quaternions

Extended classical Fibonacci identities to generalized forms

Provided formulas connecting Horadam numbers and quaternions

Abstract

In this paper, we consider the generalized Fibonacci quaternion which is the Horadam quaternion sequence. Then we used the Binet's formula to show some properties of the Horadam quaternion. We get some generalized identities of the Horadam number and generalized Fibonacci quuaternion.