KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 6

On recursive hyperbolic functions in Fibonacci-Lucas sense

Ahmet Daşdemir
Tuncay Deniz Şentürk
Zafer Ünal
Sayfa
2046–2062
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Further, we present many identities and hyperbolic properties of our new definitions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The hyperbolic Fibonacci and hyperbolic Lucas functions have been introduced before and have been improved to functions of the symmetrical form.
📊
Temel Bulgular & Veri:In this paper, we generalize the mentioned definitions, which will be called Horadam hyperbolic sine function $ \left( HSF \right) $ and Horadam hyperbolic cosine function $ \left( HCF \right) $.
💡
Sonuç & Katkı:Further, we present many identities and hyperbolic properties of our new definitions.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Horadam hyperbolic function · Horadam spiral · quasi-sine Horadam function

Abstract

The hyperbolic Fibonacci and hyperbolic Lucas functions have been introduced before and have been improved to functions of the symmetrical form. In this paper, we generalize the mentioned definitions, which will be called Horadam hyperbolic sine function $ \left( HSF \right) $ and Horadam hyperbolic cosine function $ \left( HCF \right) $. Further, we present many identities and hyperbolic properties of our new definitions.

🔖

Bu Makaleye Atıf Yap

Daşdemir, A., Şentürk, T. D., Ünal, Z. (2022). On recursive hyperbolic functions in Fibonacci-Lucas sense. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 6, 2046–2062. https://ajindex.com/articles/529632

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. H. Bulut, Y. Pandir, and H.M. Baskonus, Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order, AIP Conf. Proc. 1558 (1), 1914–1918, 2013
  2. S.M. Ege and E. Misirli, The modified Kudryashov method for solving some fractional-order nonlinear equations, Adv. Differ. Equ. 2014, Art. No. 135, 2014
  3. S. Falcón and Á. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32 (5), 1615–1624, 2007
  4. S. Falcón and Á. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals, 38 (2), 409–420, 2008
  5. A.F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly, 68 (5), 455– 459, 1961
  6. A.F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke. Math. J. 32 (3), 437–446, 1965
  7. A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (3), 161–176, 1965
  8. A.F. Horadam, Special properties of the sequence ${W_n}\left( {a,b;p,q} \right)$, Fibonacci Quart. 5 (3), 424–434, 1967
  9. T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Inc., Hoboken, NJ, 2019
  10. Y. Pandir, Y. Gurefe, and E. Misirli, A new approach to Kudryashov’s method for solving some nonlinear physical models, Int. J. Phys. Sci. 7 (21), 2860–2866, 2012
  11. S.S. Ray, New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods, Chinese Physics B. 25 (4), 040204, 2016
  12. A.P. Stakhov, Hyperbolic Fibonacci and Lucas functions: a new mathematics for the living nature, ITI, Vinnitsa, 2003
  13. A.P. Stakhov and S. Aranson, Hyperbolic Fibonacci and Lucas functions, “Golden” Fibonacci goniometry, Bodnar’s geometry, and Hilbert’s fourth problem, Appl. Math. 2, 74–84, 2011
  14. A.P. Stakhov and B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23, 379–389, 2005
  15. A.P. Stakhov and B. Rozin, The Golden Shofar, Chaos Solitons Fractals, 26 (3), 677-684, 2005
  16. A.P. Stakhov and B. Rozin, The “golden” hyperbolic models of Universe, Chaos Solitons Fractals, 34 (2), 159–171, 2007
  17. A.P. Stakhov and I.S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci. 208, 9–14, 1993.