Gelin-Cesáro identities for Fibonacci and Lucas quaternions

Ahmet Daşdemir

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2019)

  • Volume: 18, page 137-144
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Ahmet Daşdemir. "Gelin-Cesáro identities for Fibonacci and Lucas quaternions." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 18 (2019): 137-144. <http://eudml.org/doc/296831>.

@article{AhmetDaşdemir2019,
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.},
author = {Ahmet Daşdemir},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {Fibonacci quaternion; Gelin-Cesáro identity; Catalan’s identity},
language = {eng},
pages = {137-144},
title = {Gelin-Cesáro identities for Fibonacci and Lucas quaternions},
url = {http://eudml.org/doc/296831},
volume = {18},
year = {2019},
}

TY - JOUR
AU - Ahmet Daşdemir
TI - Gelin-Cesáro identities for Fibonacci and Lucas quaternions
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2019
VL - 18
SP - 137
EP - 144
AB - 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.
LA - eng
KW - Fibonacci quaternion; Gelin-Cesáro identity; Catalan’s identity
UR - http://eudml.org/doc/296831
ER -

References

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  1. Horadam, A.F. "Complex Fibonacci numbers and Fibonacci quaternions." Amer. Math. Monthly 70 (1963): 289-291. 
  2. Falcón, Sergio and Ángel Plaza. "On the Fibonacci k-numbers." Chaos Solitons Fractals 32, no. 5 (2007): 1615-1624. 
  3. 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. 
  4. 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. 
  5. Halici, Serpil. "On Fibonacci quaternions." Adv. Appl. Clifford Algebr. 22, no. 2 (2012): 321-327. 
  6. Iyer, Muthulakshmi R. "Some results on Fibonacci quaternions." Fibonacci Quart. 7 (1969): 201-210. 
  7. Iyer, Muthulakshmi R. "A note on Fibonacci quaternions." Fibonacci Quart. 7, no. 3 (1969): 225-229. 
  8. Falcon, Sergio. "On the k-Lucas numbers." Int. J. Contemp. Math. Sci. 6, no. 21-24 (2011): 1039-1050. 
  9. 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. 
  10. Swamy, M.N.S. "On generalized Fibonacci quaternions." Fibonacci Quart. 11, no. 5 (1973): 547-549. 
  11. Tan, Elif, Semih Yilmaz and Murat Sahin. "On a new generalization of Fibonacci quaternions." Chaos Solitons Fractals 82 (2016): 1-4. 

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