Title

A NOTE ON BICOMPLEX FIBONACCI
AND LUCAS NUMBERS

Authors

Semra Kaya Nurkan, İlkay Arslan Güven
Department of Mathematics
Uşak University
64200, Uşak, TURKEY
Department of Mathematics
Gaziantep University
27310, Gaziantep, TURKEY

Abstract

In this study, we define a new type of Fibonacci and Lucas numbers which are called bicomplex Fibonacci and bicomplex Lucas numbers. We obtain the well-known properties e.g. D'ocagnes, Cassini, Catalan for these new types. We also give the identities of negabicomplex Fibonacci and negabicomplex Lucas numbers, Binet formulas and relations of them.

History

Received: February 21, 2017
Revised: March 28, 2018
Published: November 29, 2018

AMS Classification, Key Words

AMS Subject Classification: 11B39, 11E88, 11R52
Key Words and Phrases: Fibonacci numbers, Lucas numbers, bicomplex numbers

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Bibliography

1

M. Akyiğit, H.H. Kösal and M. Tosun, Split Fibonacci quaternions, Adv. in Appl. Clifford Algebras, 23 (2013), 535-545, doi 10.1007/s00006-013-0401-9.

2

W. K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc., 4 (1873), 381-395.

3

R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Pub. Co. Pte. Ltd., (1997).

4

H. W. Guggenheimer, Differential Geometry,

How to Cite?

DOI: 10.12732/ijpam.v120i3.7 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 3
Pages: 365 - 377

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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