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Dergiler / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 1

De Moivre-Type Identities for the Pell Numbers

Seda YAMAÇ AKBIYIK
Mücahit AKBIYIK
Sayfa
63–67
Yayın Tarihi
2022-11-02
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In addition, we define a Pell sequence with new initial conditions and give some identities for these third order Pell numbers such as Binet's formulas, generating functions, sums.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers.Moreover, we obtain the De Moivre-type identities for these numbers.
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Temel Bulgular & Veri:This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers.Moreover, we obtain the De Moivre-type identities for these numbers.
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Sonuç & Katkı:In addition, we define a Pell sequence with new initial conditions and give some identities for these third order Pell numbers such as Binet's formulas, generating functions, sums.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

This paper aims to present a method for constructing the second order Pell and Pell-Lucas numbers and the third order Pell and Pell-Lucas numbers.Moreover, we obtain the De Moivre-type identities for these numbers. In addition, we define a Pell sequence with new initial conditions and give some identities for these third order Pell numbers such as Binet's formulas, generating functions, sums.

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Bu Makaleye Atıf Yap

AKBIYIK, S. Y., AKBIYIK, M. (2022). De Moivre-Type Identities for the Pell Numbers. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 1, 63–67. https://ajindex.com/articles/609071

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Kaynakça (12)

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  6. Kılıç, E., Taşcı, D., The generalized Binet formula, representation and sums of the generalized order- Pell numbers, Taiwanese J. Math., 10 (6)(2006), 1661–1670
  7. Kılıç, E., The generalized order- k Fibonacci - Pell sequence by matrix methods, Journal of Computational and Applied Mathematics, 209(2)(2007), 133–145
  8. Pethö, A., The Pell sequence contains only trivial perfect powers, In Colloquia on Sets, Graphs and Numbers, Soc. Math., J´anos Bolyai, North-Holland, Amsterdam (1991), 561–568
  9. Pin-Yen, L., De Moivre-Type Identities for the Tribonacci Numbers, The Fibonacci Quarterly, 2(1988), 131–134
  10. Pin-Yen, L., De Moivre-Type Identities for the Tetranacci Numbers, In: Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht(1991),
  11. Sloane, N.J.A., The on-line encyclopedia of integer sequences,
  12. Soykan, Y., On Generalized third-order Pell numbers, Asian Journal of Advanced Research and Reports, 6(1)(2019), https://doi.org/10.9734/ajarr/2019/v6i130144, 1–18.