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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2026 / Cilt: 12 Sayı: 1

On The Properties Of The Complex Fibonacci And Lucas Numbers With Rational Subscript Via Roots Of The Fibonacci Matrix

Fikri Köken(NECMETTİN ERBAKAN ÜNİVERSİTESİ)
Pages
148–157
Publication Date
2019-03-24
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, some identities related to the complex Fibonacci and Lucas numbers with rational subscripts of the forms and are given for every integer odd n and , respectively.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we exploit general techniques from matrix theory to establish some identities for the complex Fibonacci and Lucas numbers with rational subscripts of the forms and .
📊
Key Findings & Data:For this purpose, we establish matrix functions and of the Fibonacci matrix of order for integer odd n and discuss some relations between two special matrices functions and , respectively.
💡
Conclusion & Impact:Also, some identities related to the complex Fibonacci and Lucas numbers with rational subscripts of the forms and are given for every integer odd n and , respectively.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci dizileri · Matris fonksiyonları · Kök matrisleri

Abstract

In this study, we exploit general techniques from matrix theory to establish some identities for the complex Fibonacci and Lucas numbers with rational subscripts of the forms and . For this purpose, we establish matrix functions and of the Fibonacci matrix of order for integer odd n and discuss some relations between two special matrices functions and , respectively. Also, some identities related to the complex Fibonacci and Lucas numbers with rational subscripts of the forms and are given for every integer odd n and , respectively.

Özet

Bu çalışmada, ve formlarındaki rasyonel indisli kompleks Fibonacci ve Lucas sayıları için bazı eşitlikler oluşturmak için matris teorisinden genel tekniklerden faydalanırız. Bu amaçla, tek n tam sayıları için mertebeden Fibonacci matrisinin and matris fonksiyonlarını kurar ve sırasıyla and iki özel matris fonksiyonu arasındaki bazı ilişkileri ele alırız. Sırasıyla, tek n tam sayıları ve için ve formlarındaki rasyonel indisli kompleks Fibonacci ve Lucas sayıları ile ilgili bazı eşitlikler veririz.

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Cite This Article

Köken, F. (2019). On The Properties Of The Complex Fibonacci And Lucas Numbers With Rational Subscript Via Roots Of The Fibonacci Matrix. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 12 Sayı: 1, 148–157. https://doi.org/10.18185/erzifbed.431628

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References (15)

  1. Arslan, S., Köken, F. (2017). “Some Identities For The Fibonacci And Lucas Sequences With Rational Subscript Via Matrix Methods”, Bulletin Of Mathematics And Statistics Research, 5 (4), 81-87.
  2. Bicknell M. and Hoggatt, Jr. V. E. (1963). “Fibonacci Matrices and Lambda Functions”, Fibonacci Quarterly, 1 (2), 47-52.
  3. Bicknell, M. (1965). “Fibonacci fantasy: The square root of the Q matrix”, Fibonacci Quarterly, 3 (1), 67-71.
  4. Gantmacher, F.R. (1960). “The Theory of Matrices”, Volume 1. Chelsea, New York.
  5. Gould, H.W. 1981. “A history of the Fibonacci Q-matrix and a higher-dimensional problem”, Fibonacci Quarterly, 19 (3), 250-257.
  6. Halsey, E. (1965). “The Fibonacci Number where u is not an Integer”, Fibonacci Quarterly, 3 (2), 147-152.
  7. Halici S., Akyüz Z. (2016). “Fibonacci and Lucas Sequences at Negative Indices”, Konuralp Journal of Mathematics, 4 (1), 172-178.
  8. Higham, N.J. (2008). “Functions of Matrices: Theory and Computation”, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
  9. Horadam, A. F. and Shannon, A.G. (1988). “Fibonacci and Lucas Curves”, Fibonacci Quarterly, 26 (1), 3-13.
  10. Hoggatt, Jr. V. E. and Bicknell, M. (1964). Some new Fibonacci Identities, Fibonacci Quarterly, 2, (1), 29-31.
  11. Koshy, T. (2001). “Fibonacci and Lucas Numbers with Applications”, John Wiley & Sons Inc.
  12. Parker, F.D. (1968). “A Fibonacci Function”, Fibonacci Quarterly, 6 (1), 1-2.
  13. Richard, A.J. (1991). “Generalized Complex Fibonacci and Lucas Functions”, Fibonacci Quarterly, 29 (1), 13-18.
  14. Vajda, S. (1989). “Fibonacci, Lucas numbers, and the golden section Theory and Applications”. Dover Publications Inc, Mineola N.Y., ISBN-13: 978-0486462769.
  15. Wituła, R. (2011). “Fibonacci and Lucas Numbers for Real Indices and Some Applications”, Acta Physica Polonica A, 120 (4), 755-758.