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On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients

Yıl 2020, Cilt: 8 Sayı: 1, 55 - 68, 20.03.2020

Arzu Cihan Ayşe Zeynep Azak , Mehmet Ali Güngör

https://doi.org/10.36753/mathenot.621602

Öz

In this paper, dual-complex Fibonacci numbers with generalized Fibonacci and Lucas coefficients are dened. Generating function is given for this number system. Binet formula is obtained by the help of this generating function. Then, well-known Cassini, Catalan, d'Ocagne's, Honsberger, Tagiuri and other identities are given for this number system. Finally, it is seen that the theorems and the equations which are obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].

Anahtar Kelimeler

Dual-complex numbers generalized Fibonacci

Kaynakça

  • [1] Dunlap R.A.: The Golden Ratio and Fibonacci Numbers. World Scientific Publishing Co. Pte. Ltd., Singapore (1997).
  • [2] Gungor M.A. and Azak A.Z.: Investigation of Dual-complex Fibonacci, Dual-complex Lucas Numbers and Their Properties. Adv. Appl. Clifford Algebras 27, 3083{3096, (2017).
  • [3] Hoggatt Jr. V.E.: Fibonacci and Lucas Numbers. Houghton-Mifflin Co.,Boston (1969).
  • [4] Horadam A.F.: A Generalized Fibonacci Sequence. Amer. Math. Monthly 68, 455{459, (1961).
  • [5] Iakini A.L.: Generalized Quaternions of Higher Order.Fibonacci Quart. 15, 343{346, (1977).
  • [6] Koshy T.: Fibonacci and Lucas Numbers with Applications. Wiley and Sons Publication, New York (2001).
  • [7] Majernik V.: Multicomponent Number Systems. Acta Phys. Pol. A 90(3), 491{498 (1996).
  • [8] Messelmi F.: Dual-complex Numbers and Their Holomorphic Functions. https://hal.archives-ouvertes.fr/hal-01114178, (2015).
  • [9] Scholfield P.H.: The Theory of Proportion in Architecture. Cambridge University Press, Cambridge (1958).
  • [10] Silvester J.R.: Fibonacci Properties by Matrix Methods.Math. Gaz. 63(425), 188{191, (1979).
  • [11] Yuce S. and Aydın Torunbalcı, F.: Generalized Dual Fibonacci Quaternions. Appl. Math. E-Notes 16, 276{289, (2016).

Yıl 2020, Cilt: 8 Sayı: 1, 55 - 68, 20.03.2020

Arzu Cihan Ayşe Zeynep Azak , Mehmet Ali Güngör

https://doi.org/10.36753/mathenot.621602

Öz

Kaynakça

  • [1] Dunlap R.A.: The Golden Ratio and Fibonacci Numbers. World Scientific Publishing Co. Pte. Ltd., Singapore (1997).
  • [2] Gungor M.A. and Azak A.Z.: Investigation of Dual-complex Fibonacci, Dual-complex Lucas Numbers and Their Properties. Adv. Appl. Clifford Algebras 27, 3083{3096, (2017).
  • [3] Hoggatt Jr. V.E.: Fibonacci and Lucas Numbers. Houghton-Mifflin Co.,Boston (1969).
  • [4] Horadam A.F.: A Generalized Fibonacci Sequence. Amer. Math. Monthly 68, 455{459, (1961).
  • [5] Iakini A.L.: Generalized Quaternions of Higher Order.Fibonacci Quart. 15, 343{346, (1977).
  • [6] Koshy T.: Fibonacci and Lucas Numbers with Applications. Wiley and Sons Publication, New York (2001).
  • [7] Majernik V.: Multicomponent Number Systems. Acta Phys. Pol. A 90(3), 491{498 (1996).
  • [8] Messelmi F.: Dual-complex Numbers and Their Holomorphic Functions. https://hal.archives-ouvertes.fr/hal-01114178, (2015).
  • [9] Scholfield P.H.: The Theory of Proportion in Architecture. Cambridge University Press, Cambridge (1958).
  • [10] Silvester J.R.: Fibonacci Properties by Matrix Methods.Math. Gaz. 63(425), 188{191, (1979).
  • [11] Yuce S. and Aydın Torunbalcı, F.: Generalized Dual Fibonacci Quaternions. Appl. Math. E-Notes 16, 276{289, (2016).
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Arzu Cihan

Ayşe Zeynep Azak

Mehmet Ali Güngör 0000-0003-1863-3183

Yayımlanma Tarihi 20 Mart 2020
Gönderilme Tarihi 18 Eylül 2019
Kabul Tarihi 14 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

APA Cihan, A., Azak, A. Z., & Güngör, M. A. (2020). On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes, 8(1), 55-68. https://doi.org/10.36753/mathenot.621602
AMA Cihan A, Azak AZ, Güngör MA. On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Math. Sci. Appl. E-Notes. Mart 2020;8(1):55-68. doi:10.36753/mathenot.621602
Chicago Cihan, Arzu, Ayşe Zeynep Azak, ve Mehmet Ali Güngör. “On Dual-Complex Numbers With Generalized Fibonacci and Lucas Numbers Coefficients”. Mathematical Sciences and Applications E-Notes 8, sy. 1 (Mart 2020): 55-68. https://doi.org/10.36753/mathenot.621602.
EndNote Cihan A, Azak AZ, Güngör MA (01 Mart 2020) On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes 8 1 55–68.
IEEE A. Cihan, A. Z. Azak, ve M. A. Güngör, “On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients”, Math. Sci. Appl. E-Notes, c. 8, sy. 1, ss. 55–68, 2020, doi: 10.36753/mathenot.621602.
ISNAD Cihan, Arzu vd. “On Dual-Complex Numbers With Generalized Fibonacci and Lucas Numbers Coefficients”. Mathematical Sciences and Applications E-Notes 8/1 (Mart 2020), 55-68. https://doi.org/10.36753/mathenot.621602.
JAMA Cihan A, Azak AZ, Güngör MA. On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Math. Sci. Appl. E-Notes. 2020;8:55–68.
MLA Cihan, Arzu vd. “On Dual-Complex Numbers With Generalized Fibonacci and Lucas Numbers Coefficients”. Mathematical Sciences and Applications E-Notes, c. 8, sy. 1, 2020, ss. 55-68, doi:10.36753/mathenot.621602.
Vancouver Cihan A, Azak AZ, Güngör MA. On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Math. Sci. Appl. E-Notes. 2020;8(1):55-68.
 Kapak Resmi İndir

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