The Pell and Pell-Lucas Numbers via Square Roots of Matrices

Authors

  • Saadet Arslan Department of Mathematics, Ahmet Kelesoglu Faculty of Education, Necmettin Erbakan University, Konya
  • Fikri Köken Konya Ereğli Kemal Akman Vocational School, Necmettin Erbakan University, Konya

DOI:

https://doi.org/10.26713/jims.v8i3.393

Keywords:

Pell and Pell-Lucas Numbers, Square Roots of Matrices

Abstract

In this paper, the Pell and Pell-Lucas numbers with specialized rational subscripts are derived from general expressions by square roots of the matrices \(M^n\) and \(N^n\). Besides, we reveal that the identities involving these numbers are produced by square roots of matrices \(M^{n/2}\) and \(N^{n/2}\). Further we show that the matrices \(M^n\) and \(N^n\) are generalized to rational powers by using the Abel's functional equation.

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References

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Published

2016-11-09
CITATION

How to Cite

Arslan, S., & Köken, F. (2016). The Pell and Pell-Lucas Numbers via Square Roots of Matrices. Journal of Informatics and Mathematical Sciences, 8(3), 159–166. https://doi.org/10.26713/jims.v8i3.393

Issue

Vol. 8 No. 3 (2016)

Section

Research Articles

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