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The k-Fibonacci hyperbolic functions

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  • Falcón, Sergio
  • Plaza, Ángel

Abstract

An extension of the classical hyperbolic functions is introduced and studied. These new k-Fibonacci hyperbolic functions generalize also the k-Fibonacci sequences, say {Fk,n}n=0∞, recently found by studying the recursive application of two geometrical transformations onto C¯=C∪{+∞} used in the well-known four-triangle longest-edge (4TLE) partition. In this paper, several properties of these k-Fibonacci hyperbolic functions are studied in an easy way. We finalize with the introduction of some curves and surfaces naturally related with the k-Fibonacci hyperbolic functions.

Suggested Citation

  • Falcón, Sergio & Plaza, Ángel, 2008. "The k-Fibonacci hyperbolic functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 409-420.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:409-420
    DOI: 10.1016/j.chaos.2006.11.019
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    References listed on IDEAS

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    6. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
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    Cited by:

    1. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    2. Falcón, Sergio & Plaza, Ángel, 2009. "On k-Fibonacci sequences and polynomials and their derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1005-1019.
    3. Koshkin, Sergiy & Styers, Taylor, 2017. "From golden to unimodular cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 208-214.
    4. Nalli, Ayse & Haukkanen, Pentti, 2009. "On generalized Fibonacci and Lucas polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3179-3186.
    5. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    6. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    7. Ilija Tanackov & Ivan Pavkov & Željko Stević, 2020. "The New New-Nacci Method for Calculating the Roots of a Univariate Polynomial and Solution of Quintic Equation in Radicals," Mathematics, MDPI, vol. 8(5), pages 1-18, May.

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