Fundamental properties of extended Horadam numbers

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.

On Fibonacci quaternion matrix

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.

On the Fibonacci quaternion sequence with quadruple-produce components

This paper examines the Fibonacci quaternion sequence with quadruple-produce components, and demonstrates a golden-like ratio and some identities for this sequence. Its generating and exponential generating functions are given. Along with these, its series and binomial sum formula are established.

SOME PROPERTIES OF BIVARIATE FIBONACCI AND LUCAS QUATERNION POLYNOMIALS

In this work, we introduce bivariate Fibonacci quaternion polynomials andbivariate Lucas quaternion polynomials. We present generating function,Binet formula, matrix representation, binomial formulas and some basicidentities for the bivariate Fibonacci and Lucas quaternion polynomialsequences. Moreover we give various kinds of sums for these quaternionpolynomials.

Horadam 2k-ions

In this paper, we generalize Fibonacci quaternion, octonion, sedenion, trigintaduonion, etc. and define Horadam 2^{k}-ions and investigate their properties. Each Horadam (such as Fibonacci, Lucas, Pell) quaternions, octonions and sedenions are Horadam 2^{k}-ions. We also present connection to some earlier works.