On h(x)-Fibonacci polynomials in an arbitrary algebra

Abstract

In this paper, we introduce h(x)-Fibonacci polynomials in an arbitrary finite-dimensional unitary algebra over a field K (K = R,C), which generalize both h(x)-Fibonacci quaternion polynomials and h(x)-Fibonacci octonion polynomials. For h(x)-Fibonacci polynomials in such an arbitrary algebra, we prove summation formula, generating function, Binet-style formula, Catalan-style identity, and d Ocagne-type identity.