The (s, t)−Jacobsthal Hybrid Numbers and (s, t)−Jacobsthal-Lucas Hybrid Numbers

Abstract

In this thesis, we study the (s, t)−Jacobsthal sequence, (s, t)−Jacobsthal-Lucas sequence and hybid numbers to establish definition of two new numbers called (s, t)−Jacobsthal hybrid numbers, denoted by Hj_n(s, t), and (s, t)−Jacobsthal-Lucas hybrid numbers, denoted by Hc_n(s, t), defined by Hj_n(s, t) = j_n(s, t) + ij_n+1(s, t) + εj_n+2(s, t) + hj_n+3(s, t) (1) and Hcn(s, t) = c_n(s, t) + ic_n+1(s, t) + εc_n+2(s, t) + hc_n+3(s, t), (2) respectively, where i, ε, h are hybrid units, j_n(s, t) are (s, t)−Jacobsthal numbers and c_n(s, t) are (s, t)−Jacobsthal-Lucas numbers The main purpose of this thesis is to define, study and prove some properties of (s, t)−Jacobsthal hybrid numbers and (s, t)−Jacobsthal-Lucas hybrid numbers, such as Binet fomulas, Catalan’s identity and Cassini’s identity.