Padovan's Bicomplex Dual Quaternary Numbers
Renata Passos Machado Vieira *
Postgraduate Program in Teaching of the Northeast Education Network { Polo RENOEN-UFC, Brazil.
Francisco Regis Vieira Alves
Federal Institute of Science and Technology Education of the State of Ceara, Brazil.
Paula Maria Machado Cruz Catarino
University of Tras-os-Montes and Alto Douro, Portugal.
*Author to whom correspondence should be addressed.
Abstract
The present study generalizes the dual quaternions, called dual bicomplex quaternions of Horadam. With that, these numbers are introduced in the Padovan sequence, presenting some mathematical properties, such as the Binet formula, generating function and matrix form.
Keywords: Binet's formula, generalization, dual bicomplex quaternions, Padovan sequence