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Dual-Gaussian Pell and Pell-Lucas numbers

Yıl 2022, Cilt: 43 Sayı: 4, 665 - 671, 27.12.2022

Hasan Gökbaş

https://doi.org/10.17776/csj.1067983

Öz

In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell and Pell-Lucas numbers. Also, some sum ve product properties of Pell and Pell-Lucas numbers are given. Moreover, we obtain the Binet’s formula, generating function, d’Ocagne’s identity, Catalan’s identity, Cassini’s identity and some sum formulas for these new type numbers. Some algebraic proporties of dual-Gaussian Pell and Pell-Lucas numbers are investigated. Futhermore, we give the matrix representation of dual-Gaussian Pell and Pell-Lucas numbers.

Anahtar Kelimeler

Dual-Gaussian numbers Dual-Gaussian Pell numbers Dual- Gaussian Pell-Lucas numbers

Kaynakça

  • [1] Horadam A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Math. Monthly, 70 (1963) 289-291.
  • [2] Fjelstad P., Gal S.G., n-dimensional Dual Complex Numbers, Advances in Applied Clifford Algebras, 8(2) (1998) 309-322.
  • [3] Clifford W.K., A Preliminary Sketch of Biquaternions, (1873).
  • [4] Messelmi F., Dual Complex Numbers and Their Holomorphic Functions, https://hal.archives-ouvertes.fr/hal-01114178. Retrieved January 7, 2022.
  • [5] Catarino P., Bicomplex k-Pell Quaternions, Computational Methods and Function Theory, 19 (2019) 65-76.
  • [6] Gül K., Dual Bicomplex Horadam Quaternions, Notes on Numbers Theory and Discrete Mathematics, 26 (2020) 187-205.
  • [7] Soykan S., On Dual Hyperbolic Generalized Fibonacci Numbers, Indian Journal of Pure and Applied Mathematics, 52 (2021) 62-78.
  • [8] Vajda S., Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood Limited Publ., England, (1989).
  • [9] Matsuda G., Kaji S. Ochiai H., Anti-commutative Dual Complex Numbers and 2 Rigid Transformation in Mathematical Progress in Expressive Inage Synthesis I. Springer, (2014). [10] Akar M., Yüce S., Şahin S., On the Dual Hyperbolic Numbers and the Complex Hyperbolic numbers, Journal of Computer Science & Computational Mathematics, 8 (2018) 1-6.
  • [11] Majernik V., Multicomponent Number Systems, Acta Physica Polonica A., 90(3) (1996) 491-498.
  • [12] Aydın F.T., Dual-complex k-Fibonacci Numbers, Chaos, Solitons & Fractals, 115 (2018) 1-6.
  • [13] Koshy T., Fibonacci and Lucas Numbers with Applications, A Wiley-Intersience Publication, USA, (2001).
  • [14] Koshy T., Pell and Pell-Lucas Numbers with Applications, Springer New York Heidelberg Dordrecht, London, (2014).
  • [15] Halıcı S., Çürük Ş., On Dual k-bicomplex Numbers and Some Identities Including Them, Fundamental Journal of Mathematics and Applications, 3 (2020) 86-93.
  • [16] Azak Z., Güngör M.A., Investigation of Dual-complex Fibonacci, Dual-complex Lucas Numbers and Their Properties, Adv. Appl. Clifford Algebras, 27 (2017) 3083-3096.
  • [17] Aydın F.T., Dual-complex k-Pell Quaternions, Notes on Numbers Theory and Discrete Mathematics, 25 (2019) 111-125.

Yıl 2022, Cilt: 43 Sayı: 4, 665 - 671, 27.12.2022

Hasan Gökbaş

https://doi.org/10.17776/csj.1067983

Öz

Kaynakça

  • [1] Horadam A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, American Math. Monthly, 70 (1963) 289-291.
  • [2] Fjelstad P., Gal S.G., n-dimensional Dual Complex Numbers, Advances in Applied Clifford Algebras, 8(2) (1998) 309-322.
  • [3] Clifford W.K., A Preliminary Sketch of Biquaternions, (1873).
  • [4] Messelmi F., Dual Complex Numbers and Their Holomorphic Functions, https://hal.archives-ouvertes.fr/hal-01114178. Retrieved January 7, 2022.
  • [5] Catarino P., Bicomplex k-Pell Quaternions, Computational Methods and Function Theory, 19 (2019) 65-76.
  • [6] Gül K., Dual Bicomplex Horadam Quaternions, Notes on Numbers Theory and Discrete Mathematics, 26 (2020) 187-205.
  • [7] Soykan S., On Dual Hyperbolic Generalized Fibonacci Numbers, Indian Journal of Pure and Applied Mathematics, 52 (2021) 62-78.
  • [8] Vajda S., Fibonacci and Lucas Numbers and the Golden Section, Ellis Horwood Limited Publ., England, (1989).
  • [9] Matsuda G., Kaji S. Ochiai H., Anti-commutative Dual Complex Numbers and 2 Rigid Transformation in Mathematical Progress in Expressive Inage Synthesis I. Springer, (2014). [10] Akar M., Yüce S., Şahin S., On the Dual Hyperbolic Numbers and the Complex Hyperbolic numbers, Journal of Computer Science & Computational Mathematics, 8 (2018) 1-6.
  • [11] Majernik V., Multicomponent Number Systems, Acta Physica Polonica A., 90(3) (1996) 491-498.
  • [12] Aydın F.T., Dual-complex k-Fibonacci Numbers, Chaos, Solitons & Fractals, 115 (2018) 1-6.
  • [13] Koshy T., Fibonacci and Lucas Numbers with Applications, A Wiley-Intersience Publication, USA, (2001).
  • [14] Koshy T., Pell and Pell-Lucas Numbers with Applications, Springer New York Heidelberg Dordrecht, London, (2014).
  • [15] Halıcı S., Çürük Ş., On Dual k-bicomplex Numbers and Some Identities Including Them, Fundamental Journal of Mathematics and Applications, 3 (2020) 86-93.
  • [16] Azak Z., Güngör M.A., Investigation of Dual-complex Fibonacci, Dual-complex Lucas Numbers and Their Properties, Adv. Appl. Clifford Algebras, 27 (2017) 3083-3096.
  • [17] Aydın F.T., Dual-complex k-Pell Quaternions, Notes on Numbers Theory and Discrete Mathematics, 25 (2019) 111-125.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Natural Sciences
Yazarlar

Hasan Gökbaş 0000-0002-3323-8205

Yayımlanma Tarihi 27 Aralık 2022
Gönderilme Tarihi 3 Şubat 2022
Kabul Tarihi 2 Ekim 2022
Yayımlandığı Sayı Yıl 2022Cilt: 43 Sayı: 4

Kaynak Göster

APA Gökbaş, H. (2022). Dual-Gaussian Pell and Pell-Lucas numbers. Cumhuriyet Science Journal, 43(4), 665-671. https://doi.org/10.17776/csj.1067983
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