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

Abstract

In this paper, dual-complex Fibonacci numbers with generalized Fibonacci and Lucas coefficients aredefined. Generating function is given for this number system. Binet’s formula is obtained by the help ofthis generating function. Then, well-known Cassini, Catalan, d’Ocagne’s, Honsberger, Tagiuri and otheridentities are given for this number system. Finally, it is seen that the theorems and the equations whichare obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].