On dual Horadam octonions

Abstract

In this paper, we introduce the dual Horadam octonions, we give the Binet formula, generating function, exponential generating function, summation formula, Catalan's identity, Cassini's identity and d'Ocagne's identity of dual Horadam octonions. Employing these results, we present the Binet formula, generating function, summation formula, Catalan, Cassini and d'Ocagne identities for dual Fibonacci, dual Lucas, dual Jacobsthal, dual Jacobsthal-Lucas, dual Pell and dual Pell-Lucas octonions. So we generalize results that were obtained earlier by scientists. Finally, we introduce the matrix generator for dual Horadam octonions and this generator gives the Cassini formula for the dual Horadam octonions.