On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients

Abstract

In this paper, dual-complex Fibonacci numbers with generalized Fi bonacci and Lucas coefficients are dened. Generating function is given for  this number system. Binet formula is obtained by the help of this generat ing function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger,  Tagiuri and other identities are given for this number system. Finally, it  is seen that the theorems and the equations which are obtained for the  special values p = 1 and q = 0 correspond to the theorems and identities  in [2].