KaydedilenlerDerginizi ekleyin

Dergiler / Gazi University Journal of Science / 2026 / Volume: 34 Issue: 2

Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

Miraç Çetin(BAŞKENT ÜNİVERSİTESİ)0000-0002-9588-0295
Can Kızılateş(BÜLENT ECEVİT ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ)0000-0002-7958-4226
Fatma Yeşil Baran(AMASYA UNIVERSITY)0000-0001-8613-2706
Naim Tuglu(GAZİ ÜNİVERSİTESİ)0000-0002-7277-0034
Sayfa
—
Yayın Tarihi
2021-06-01
🏛️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)

Moreover, with the help of concept of Riordan array, we obtain the generating functions for these numbers and a variety of identities are derived.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:This paper is concerned with the combinatorial identities of the harmonic and the hyperharmonic Fibonacci numbers.
📊
Temel Bulgular & Veri:By using the symmetric algorithm, we get some identities which improve the usual results and generalize known equations.
💡
Sonuç & Katkı:Moreover, with the help of concept of Riordan array, we obtain the generating functions for these numbers and a variety of identities are derived.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Hyperharmonic · Fibonacci numbers · Symmetric

Abstract

This paper is concerned with the combinatorial identities of the harmonic and the hyperharmonic Fibonacci numbers. By using the symmetric algorithm, we get some identities which improve the usual results and generalize known equations. Moreover, with the help of concept of Riordan array, we obtain the generating functions for these numbers and a variety of identities are derived.

🔖

Bu Makaleye Atıf Yap

Çetin, M., Kızılateş, C., Baran, F. Y., Tuglu, N. (2021). Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers. Gazi University Journal of Science, Volume: 34 Issue: 2. https://doi.org/10.35378/gujs.705885

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (20)

  1. Conway, J. H., Guy, R. K., “The book of numbers”, Springer, New York, (1996).
  2. Dumont, D., “Matrices d'Euler-Seidel”, Semin. Lothar. Comb., 5 (1981).
  3. Dil, A., Mezö, I., “A symmetric algorithm for hyperharmonic and Fibonacci numbers”, Appl. Math. Comput., 206: 942-951, (2008).
  4. Bahşi, M., Mezö, I., Solak, S., “A symmetric algorithm for hyper-Fibonacci and hyper-Lucas numbers”, Ann. Math. Inform., 43:19-27, (2014).
  5. Mezö, I., Ramirez, J. L., “A q-Symmetric algorithm and its applications to some combinatorial sequences”, Online J. Anal. Comb., 12: 1-13, (2017).
  6. Dil, A., Kurt, V., “Investigating geometric and exponential polynomials with Euler-Seidel matrices”, J. Integer Seq., 14: 1-12, (2011).
  7. Dil, A., Mezö, I., “Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence”, Cent. Eur. J. Math., 7(2): 310-321, (2009).
  8. Ramirez, J. L., Shattuck, M., “A multi-parameter generalization of the symmetric algorithm”, Math. Slovaca, 68(4): 699-712, (2018).
  9. Holliday, S., Komatsu, T., “On the sum of reciprocal generalized Fibonacci numbers”, Integers, 11: 441-455, (2011).
  10. Ohtsuka, H., Nakamura, S., “On the sum of reciprocal Fibonacci numbers”, Fibonacci Quart., 46 (2):153-159, (2008).
  11. Rabinowitz, S., “Algorithmic summation reciprocals of products of Fibonacci numbers”, Fibonacci Quart., 37: 122-127, (1999).
  12. Tuglu, N., Kızılateş, C., Kesim, S., “On the harmonic and hyperharmonic Fibonacci numbers”, Adv. Difference Equ., 2015: 297, (2015).
  13. Tuglu, N., Kızılateş C., “On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers”, J.Inequal. Appl., 2015: 253, (2015).
  14. Tuglu, N., Kızılateş, C., “On the norms of some special matrices with the harmonic Fibonacci numbers”, Gazi University Journal of Science, 28 (3): 447-501, (2015).
  15. Shapiro, L. Getu, W. S., Woan, W. J., Woodson, L. C., “The Riordan group”, Discrete Appl. Math., 34: 229-239, (1991).
  16. Cheon, G. S., Hwang, S. G., Lee, S. G., “Several polynomials associated with the harmonic numbers”, Discrete Appl.Math., 155: 2573-2584, (2007).
  17. Cheon, G. S., Mikkawy, M. E. A., “Generalized harmonic numbers with Riordan arrays”, J. Number Theory, 128: 413-425, (2008).
  18. Munarini, E., “Riordan matrices and sums of harmonic numbers”, Appl. Anal. Discrete Math., 5: 176-200, (2011).
  19. Matala-Aho, T. and Vaananen, K., “On Approximation Measures of q-Logarithms”, Bull. Austral. Math. Soc., 58: 15-31, (1998).
  20. Murty, M. R., “The Fibonacci Zeta Function, Automorphic Representations and L-Functions”, Tata Institue of Fundamental Research, Hindustan Book Agency, New Delhi, 1-17, (2013).