Gelin-Cesáro identities for Fibonacci and Lucas quaternions

Ahmet Daşdemir

Abstract


To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.

Keywords


Fibonacci quaternion; Gelin-Cesáro identity; Catalan’s identity.

Mathematics Subject Classification (2010)


11B37; 16H05; 11R52

References


Horadam, A.F. "Complex Fibonacci numbers and Fibonacci quaternions." Amer. Math. Monthly 70 (1963): 289-291.

Falcón, Sergio and Ángel Plaza. "On the Fibonacci k-numbers." Chaos Solitons Fractals 32, no. 5 (2007): 1615-1624.

Ramírez, José L. "Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions." An. Stiint. Univ. "Ovidius” Constanta Ser. Mat. 23, no. 2 (2015): 201-212.

Polatlı, Emrah and Seyhun Kesim. "A note on Catalan’s identity for the k-Fibonacci quaternions." J. Integer Seq. 18, no. 8 (2015): Article 15.8.2.

Halici, Serpil. "On Fibonacci quaternions." Adv. Appl. Clifford Algebr. 22, no. 2 (2012): 321-327.

Iyer, Muthulakshmi R. "Some results on Fibonacci quaternions." Fibonacci Quart. 7 (1969): 201-210.

Iyer, Muthulakshmi R. "A note on Fibonacci quaternions." Fibonacci Quart. 7, no. 3 (1969): 225-229.

Falcon, Sergio. "On the k-Lucas numbers." Int. J. Contemp. Math. Sci. 6, no. 21-24 (2011): 1039-1050.

Fairgrieve, Steve and Henry W. Gould. "Product difference Fibonacci identities of Simson, Gelin-Cesaro, Tagiuri and generalizations." Fibonacci Quart. 43, no. 2 (2005): 137-141.

Swamy, M.N.S. "On generalized Fibonacci quaternions." Fibonacci Quart. 11, no. 5 (1973): 547-549.

Tan, Elif, Semih Yilmaz and Murat Sahin. "On a new generalization of Fibonacci quaternions." Chaos Solitons Fractals 82 (2016): 1-4.


Full Text: PDF

Download statistics: 755

Licencja Creative Commons
This article by Ahmet Daşdemir is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej