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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 74 Issue: 1

On some k- Oresme hybrid numbers including negative indices

Serpil Halıcı(PAMUKKALE UNIVERSITY)0000-0002-8071-0437
Elifcan Sayın(PAMUKKALE UNIVERSITY)0000-0001-5602-7681
Sayfa
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Yayın Tarihi
2025-03-08
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we derive some fundamental identities related to these numbers.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this study, we define k-Oresme hybrid numbers including negative indices and examine their properties, using the theory of number systems created by choosing the coefficients from unique number sets.
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Temel Bulgular & Veri:In this study, we define k-Oresme hybrid numbers including negative indices and examine their properties, using the theory of number systems created by choosing the coefficients from unique number sets.
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Sonuç & Katkı:Moreover, we derive some fundamental identities related to these numbers.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Oresme numbers · hybrid numbers · recurrence relations

Abstract

In this study, we define k-Oresme hybrid numbers including negative indices and examine their properties, using the theory of number systems created by choosing the coefficients from unique number sets. Moreover, we derive some fundamental identities related to these numbers.

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Bu Makaleye Atıf Yap

Halıcı, S., Sayın, E. (2025). On some k- Oresme hybrid numbers including negative indices. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 74 Issue: 1. https://doi.org/10.31801/cfsuasmas.1369953

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Kaynakça (14)

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  2. Cook, C.K., Some sums related to sums of Oresme numbers, Applications of Fibonacci Numbers, Proceedings of the Tenth International Research Conference on Fibonacci Numbers and Their Applications, Kluwer Academic Publishers, 9 (2004), 87–99. https://doi.org/10.1007/978-0-306-48517-6_10
  3. Goy, T., Shattuck, M., Fibonacci and Lucas identities from Toeplitz–Hessenberg matrices, Applications and Applied Mathematics: An International Journal (AAM), 5 14(2), (2019). https://doi.org/10.22108/toc.2020.116257.1631
  4. Halici, S., Sayın, E., Gur, Z. B., On k-Oresme Numbers with Negative Indices, Engineering (ICMASE 2022), 4-7 July 2022, Technical University of Civil Engineering Bucharest, Romania, 56 (2022). https://doi.org/10.1007/978-3031-21700-5_20
  5. Halici, S., Gur, Z. B., Sayin, E., k- Oresme Polynomials and Their Derivatives Indices, Engineering (ICMASE 2022), 4-7 July 2022, Technical University of Civil Engineering Bucharest, Romania, 58 (2022). https://doi.org/10.1007/978-3-031-21700-5_19
  6. Halici, S., Sayin, E., On some k-Oresme hybrid numbers, Utilitas Mathematica, 120 (2023), 1-11.
  7. Horadam, A. F., Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly, 3(3) (1965), 161-176. https://doi.org/10.1080/00150517.1965.12431416
  8. Horadam, A. F., Oresme numbers, Fibonacci Quarterly, 12(3) (1974), 267-271.
  9. Isbilir, Z., Gurses, N., Pentanacci and Pentanacci-Lucas hybrid numbers, Journal of Discrete Mathematical Sciences and Cryptography, (2021), 1-20. https://doi.org/10.1080/09720529.2021.1936899
  10. Oresme, N., Quaestiones super geometriam Euclidis, Brill Archive, 3 (1961). https://doi.org/10.33434/cams.1444712
  11. Ozdemir, M., Introduction to hybrid numbers, Advances in Applied Clifford Algebras, 28(1) (2018), 1-32. https://doi.org/10.1007/s00006-018-0833-3
  12. Senturk, G. Y., Gurses, N., Yuce, S., A New Look on Oresme numbers: dual-generalized complex component extension, In Conference Proceedings of Science, 4(2) (2021), https://doi.org/206214.10.33434/cams.1444712
  13. Szynal-Liana, A., The Horadam hybrid numbers, Discussiones Mathematicae: General Algebra and Applications, 38(1) (2018), 91-98. https://doi.org/10.7151/dmgaa.1287
  14. Szynal-Liana, A., Wloch, I., Oresme hybrid numbers and hybrationals, Kragujevac Journal of Mathematics, 48(5) (2024), 747-753. https://doi.org/10.46793/KgJMat2405.747SL