Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions

Adnan Karataş

doi:10.29002/asujse.1576933

EN

Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions

Öz

Fibonacci and Lucas quaternions are deeply studied in the literature after its definition by Horadam in 1963. Binet formula, generation function, Cassini, Catalan, Honsberger, and other identities for these sequences studied in different quaternion algebra types like split quaternion algebra, dual quaternion algebra, etc. Additionally, some of the generalizations for Fibonacci and Lucas quaternions are studied like k-Fibonacci quaternions, k-Lucas quaternions, Horadam quaternions, and more. However, despite being researched intensively, the summation formulas or weighted summation formulas for these sequences are not examined thoroughly. In this study, after briefly summarizing the literature, we focused on the summation and the weighted summation formulas for the Fibonacci and the Lucas quaternions. In addition, we provided generalized weighted summation formulas for the Fibonacci and Lucas quaternions. Moreover, we calculated generalized weighted summation formulas for the double coefficient Fibonacci and double coefficient Lucas quaternions which have two Fibonacci and Lucas coefficient in every unit of the quaternion, respectively.

Anahtar Kelimeler

Etik Beyan

The author declares that he has no conflict of interest.

Kaynakça

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Ayrıntılar

Birincil Dil

İngilizce

Konular

Sayısal ve Hesaplamalı Matematik (Diğer)

Bölüm

Araştırma Makalesi

Yazarlar

Adnan Karataş ^*
0000-0003-3652-5354
Türkiye

Yayımlanma Tarihi

30 Aralık 2024

Gönderilme Tarihi

31 Ekim 2024

Kabul Tarihi

27 Aralık 2024

Yayımlandığı Sayı

Yıl 2024 Cilt: 8 Sayı: 2

DOI

https://doi.org/10.29002/asujse.1576933

IZ

https://izlik.org/JA49FW29UJ

Kaynak Göster

RIS / Bibtex

APA

Karataş, A. (2024). Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions. Aksaray University Journal of Science and Engineering, 8(2), 114-121. https://doi.org/10.29002/asujse.1576933

AMA

1.Karataş A. Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions. Aksaray J. Sci. Eng. 2024;8(2):114-121. doi:10.29002/asujse.1576933

Chicago

Karataş, Adnan. 2024. “Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions”. Aksaray University Journal of Science and Engineering 8 (2): 114-21. https://doi.org/10.29002/asujse.1576933.

EndNote

Karataş A (01 Aralık 2024) Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions. Aksaray University Journal of Science and Engineering 8 2 114–121.

IEEE

[1]A. Karataş, “Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions”, Aksaray J. Sci. Eng., c. 8, sy 2, ss. 114–121, Ara. 2024, doi: 10.29002/asujse.1576933.

ISNAD

Karataş, Adnan. “Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions”. Aksaray University Journal of Science and Engineering 8/2 (01 Aralık 2024): 114-121. https://doi.org/10.29002/asujse.1576933.

JAMA

1.Karataş A. Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions. Aksaray J. Sci. Eng. 2024;8:114–121.

MLA

Karataş, Adnan. “Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions”. Aksaray University Journal of Science and Engineering, c. 8, sy 2, Aralık 2024, ss. 114-21, doi:10.29002/asujse.1576933.

Vancouver

1.Adnan Karataş. Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions. Aksaray J. Sci. Eng. 01 Aralık 2024;8(2):114-21. doi:10.29002/asujse.1576933