Preprint Article Version 1 This version is not peer-reviewed

On Dual Hyperbolic Generalized Fibonacci Numbers

Version 1 : Received: 14 October 2019 / Approved: 16 October 2019 / Online: 16 October 2019 (04:19:15 CEST)

How to cite: Soykan, Y. On Dual Hyperbolic Generalized Fibonacci Numbers. Preprints 2019, 2019100172 (doi: 10.20944/preprints201910.0172.v1). Soykan, Y. On Dual Hyperbolic Generalized Fibonacci Numbers. Preprints 2019, 2019100172 (doi: 10.20944/preprints201910.0172.v1).

Abstract

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

Subject Areas

Fibonacci numbers; Lucas numbers; dual hyperbolic numbers; dual hyperbolic Fibonacci numbers; Cassini identity

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