On Dual-Hyperbolic Numbers with Generalized Fibonacci and Lucas Numbers Components

Abstract

Dual-hyperbolic Fibonacci and Lucas numbers with Fibonacci and Lucas coefficients are introduced by Cihan et al. and some identities and theorems are given regarding modules and conjugates of these numbers. Later, generating function and Binet's formula with the help of this generating function have been derived. Also, Binet formula, Cassini's, Catalan's, d'Ocagne's, Honsberger and Tagiuri identities are found for dual-hyperbolic numbers with generalized Fibonacci and Lucas coefficients. While these operations are being done, we will benefit from the well-known Fibonacci and Lucas identities. Moreover, it is seen that the results which are obtained for the values $p = 1$ and $q = 0$ corresponds to the theorems in the article by Cihan et al.  [1].

Keywords

• Dual-hyperbolic numbers,Generalized Fibonacci numbers,Generalized Lucas numbers

References

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