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2019 | 18 | 137-144

Tytuł artykułu

Gelin-Cesáro identities for Fibonacci and Lucas quaternions

Autorzy

Treść / Zawartość

Języki publikacji

EN

Abstrakty

EN
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.

Rocznik

Tom

18

Strony

137-144

Daty

wydano
2019-07-24

Twórcy

  • Kastamonu University, Department of Mathematics

Bibliografia

  • 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.

Identyfikator YADDA

bwmeta1.element.ojs-issn-2300-133X-year-2019-volume-18-article-7949