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

Abstract

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.

Keywords

Ethical Statement

The author declares that he has no conflict of interest.

References

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Details

Primary Language

English

Subjects

Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

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

Publication Date

December 30, 2024

Submission Date

October 31, 2024

Acceptance Date

December 27, 2024

Published in Issue

Year 2024 Volume: 8 Number: 2

DOI

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

IZ

https://izlik.org/JA49FW29UJ

Cite

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

Öz

Sum and Weighted Sum Formulas for Fibonacci and Lucas Quaternions

Abstract

Keywords

Ethical Statement

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite