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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. https://doi.org/10.20944/preprints201910.0172.v1 Soykan, Y. On Dual Hyperbolic Generalized Fibonacci Numbers. Preprints 2019, 2019100172. https://doi.org/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.
Keywords
Fibonacci numbers; Lucas numbers; dual hyperbolic numbers; dual hyperbolic Fibonacci numbers; Cassini identity
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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