INVESTIGATING THE DUAL QUATERNION EXTENSION OF THE DGC LEONARDO SEQUENCE - Yilmaz, Cigdemigdem zeynep; Sacli, Gulsum yeliz (HONAM MATHEMATICAL SOC, 2024)
In this study, we introduce a new generalization of the Leonardo sequence, dual quaternions with the DGC Leonardo sequence coefficients, depending on the parameter p is an element of R. This generalization gives dual quaternions with the dual-complex Leonardo sequence for p = -1, dual quaternions with the hyper-dual Leonardo sequence for p = 0, and dual quaternions with the dual-hyperbolic Leonardo sequence for p = 1. The basic algebraic structures and some special characteristic relations are presented, as well as the Binet's formula, generating function, d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities.
Keywords: Leonardo sequence; dual quaternion; dual-generalized complex number; recurrence relation; https; GENERALIZED COMPLEX; FIBONACCI; Mathematics