On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients
Yıl: 2020 Cilt: 8 Sayı: 1 Sayfa Aralığı: 55 - 68 Metin Dili: İngilizce DOI: 10.36753/MATHENOT.621602 İndeks Tarihi: 24-03-2021
On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients
Öz: In this paper, dual-complex Fibonacci numbers with generalized Fibonacci and Lucas coefficients aredefined. Generating function is given for this number system. Binet’s formula is obtained by the help ofthis generating function. Then, well-known Cassini, Catalan, d’Ocagne’s, Honsberger, Tagiuri and otheridentities are given for this number system. Finally, it is seen that the theorems and the equations whichare obtained for the special values p = 1 and q = 0 correspond to the theorems and identities in [2].
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Dunlap, A.R.: The golden ratio and Fibonacci numbers. World Scientific Publishing Co. Pte. Ltd. Singapore (1997).
- [2] Güngör, M.A., Azak, A.Z.: Investigation of dual-complex Fibonacci, dual-complex Lucas numbers and their properties. Advances in Applied Clifford Algebras. 27 (4), 3083-3096 (2017).
- [3] Hoggatt, Jr.V.E.: Fibonacci and Lucas Numbers. Mifflin Co. Boston (1969).
- [4] Horadam, A.F.: A generalized Fibonacci sequence. The American Mathematical Monthly. 68 (5), 455-459 (1961).
- [5] Iakini, A.L.: Generalized quaternions of higher order. The Fibonacci Quarterly. 15 (4), 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 Physica Polonica Series a. 90 (3), 491-498 (1996).
- [8] Messelmi, F.: Dual-complex numbers and their holomorphic functions.https://hal.archives-ouvertes.fr/hal01114178, (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. The Mathematical Gazette. 63 (425), 188-191 (1979).
- [11] Yüce, S., Aydın Torunbalcı, F.: Generalized Dual Fibonacci Quaternions. Applied Mathematics E-Notes. 16 (30), 276-289 (2016).
APA | Sürekçi A, Azak A, Gungor M (2020). On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. , 55 - 68. 10.36753/MATHENOT.621602 |
Chicago | Sürekçi Arzu,Azak Ayşe Zeynep,Gungor Mehmet Ali On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. (2020): 55 - 68. 10.36753/MATHENOT.621602 |
MLA | Sürekçi Arzu,Azak Ayşe Zeynep,Gungor Mehmet Ali On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. , 2020, ss.55 - 68. 10.36753/MATHENOT.621602 |
AMA | Sürekçi A,Azak A,Gungor M On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. . 2020; 55 - 68. 10.36753/MATHENOT.621602 |
Vancouver | Sürekçi A,Azak A,Gungor M On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. . 2020; 55 - 68. 10.36753/MATHENOT.621602 |
IEEE | Sürekçi A,Azak A,Gungor M "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients." , ss.55 - 68, 2020. 10.36753/MATHENOT.621602 |
ISNAD | Sürekçi, Arzu vd. "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients". (2020), 55-68. https://doi.org/10.36753/MATHENOT.621602 |
APA | Sürekçi A, Azak A, Gungor M (2020). On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes, 8(1), 55 - 68. 10.36753/MATHENOT.621602 |
Chicago | Sürekçi Arzu,Azak Ayşe Zeynep,Gungor Mehmet Ali On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes 8, no.1 (2020): 55 - 68. 10.36753/MATHENOT.621602 |
MLA | Sürekçi Arzu,Azak Ayşe Zeynep,Gungor Mehmet Ali On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes, vol.8, no.1, 2020, ss.55 - 68. 10.36753/MATHENOT.621602 |
AMA | Sürekçi A,Azak A,Gungor M On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 55 - 68. 10.36753/MATHENOT.621602 |
Vancouver | Sürekçi A,Azak A,Gungor M On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 55 - 68. 10.36753/MATHENOT.621602 |
IEEE | Sürekçi A,Azak A,Gungor M "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients." Mathematical Sciences and Applications E-Notes, 8, ss.55 - 68, 2020. 10.36753/MATHENOT.621602 |
ISNAD | Sürekçi, Arzu vd. "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients". Mathematical Sciences and Applications E-Notes 8/1 (2020), 55-68. https://doi.org/10.36753/MATHENOT.621602 |