Research Article

Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

Volume: 34 Number: 2 June 1, 2021
EN

Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers

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.

Keywords

References

  1. [1] Conway, J. H., Guy, R. K., “The book of numbers”, Springer, New York, (1996).
  2. [2] Dumont, D., “Matrices d'Euler-Seidel”, Semin. Lothar. Comb., 5 (1981).
  3. [3] Dil, A., Mezö, I., “A symmetric algorithm for hyperharmonic and Fibonacci numbers”, Appl. Math. Comput., 206: 942-951, (2008).
  4. [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. [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. [6] Dil, A., Kurt, V., “Investigating geometric and exponential polynomials with Euler-Seidel matrices”, J. Integer Seq., 14: 1-12, (2011).
  7. [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. [8] Ramirez, J. L., Shattuck, M., “A multi-parameter generalization of the symmetric algorithm”, Math. Slovaca, 68(4): 699-712, (2018).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Publication Date

June 1, 2021

Submission Date

March 18, 2020

Acceptance Date

September 16, 2020

Published in Issue

Year 2021 Volume: 34 Number: 2

APA
Çetin, M., Kızılateş, C., Yeşil Baran, F., & Tuglu, N. (2021). Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers. Gazi University Journal of Science, 34(2), 493-504. https://doi.org/10.35378/gujs.705885
AMA
1.Çetin M, Kızılateş C, Yeşil Baran F, Tuglu N. Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers. Gazi University Journal of Science. 2021;34(2):493-504. doi:10.35378/gujs.705885
Chicago
Çetin, Miraç, Can Kızılateş, Fatma Yeşil Baran, and Naim Tuglu. 2021. “Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers”. Gazi University Journal of Science 34 (2): 493-504. https://doi.org/10.35378/gujs.705885.
EndNote
Çetin M, Kızılateş C, Yeşil Baran F, Tuglu N (June 1, 2021) Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers. Gazi University Journal of Science 34 2 493–504.
IEEE
[1]M. Çetin, C. Kızılateş, F. Yeşil Baran, and N. Tuglu, “Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers”, Gazi University Journal of Science, vol. 34, no. 2, pp. 493–504, June 2021, doi: 10.35378/gujs.705885.
ISNAD
Çetin, Miraç - Kızılateş, Can - Yeşil Baran, Fatma - Tuglu, Naim. “Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers”. Gazi University Journal of Science 34/2 (June 1, 2021): 493-504. https://doi.org/10.35378/gujs.705885.
JAMA
1.Çetin M, Kızılateş C, Yeşil Baran F, Tuglu N. Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers. Gazi University Journal of Science. 2021;34:493–504.
MLA
Çetin, Miraç, et al. “Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers”. Gazi University Journal of Science, vol. 34, no. 2, June 2021, pp. 493-04, doi:10.35378/gujs.705885.
Vancouver
1.Miraç Çetin, Can Kızılateş, Fatma Yeşil Baran, Naim Tuglu. Some Identities of Harmonic and Hyperharmonic Fibonacci Numbers. Gazi University Journal of Science. 2021 Jun. 1;34(2):493-504. doi:10.35378/gujs.705885

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