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

Arzu CİHAN [1] , Ayşe Zeynep AZAK [2] , Mehmet Ali GÜNGÖR [3]

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].
Dual-complex numbers, generalized Fibonacci
• [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).
Primary Language en Engineering Articles Author: Arzu CİHAN Institution: SAKARYA ÜNİVERSİTESİCountry: Turkey Author: Ayşe Zeynep AZAK Institution: SAKARYA ÜNİVERSİTESİCountry: Turkey Orcid: 0000-0003-1863-3183Author: Mehmet Ali GÜNGÖR (Primary Author)Institution: SAKARYA ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİCountry: Turkey Publication Date : March 20, 2020
 Bibtex @research article { mathenot621602, journal = {Mathematical Sciences and Applications E-Notes}, issn = {}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2020}, volume = {8}, pages = {55 - 68}, doi = {10.36753/mathenot.621602}, title = {On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients}, key = {cite}, author = {Ci̇han, Arzu and Azak, Ayşe Zeynep and Güngör, Mehmet Ali} } APA Ci̇han, A , Azak, A , Güngör, M . (2020). On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients . Mathematical Sciences and Applications E-Notes , 8 (1) , 55-68 . DOI: 10.36753/mathenot.621602 MLA Ci̇han, A , Azak, A , Güngör, M . "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients" . Mathematical Sciences and Applications E-Notes 8 (2020 ): 55-68 Chicago Ci̇han, A , Azak, A , Güngör, M . "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients". Mathematical Sciences and Applications E-Notes 8 (2020 ): 55-68 RIS TY - JOUR T1 - On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients AU - Arzu Ci̇han , Ayşe Zeynep Azak , Mehmet Ali Güngör Y1 - 2020 PY - 2020 N1 - doi: 10.36753/mathenot.621602 DO - 10.36753/mathenot.621602 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 55 EP - 68 VL - 8 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.621602 UR - https://doi.org/10.36753/mathenot.621602 Y2 - 2020 ER - EndNote %0 Mathematical Sciences and Applications E-Notes On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients %A Arzu Ci̇han , Ayşe Zeynep Azak , Mehmet Ali Güngör %T On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients %D 2020 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 8 %N 1 %R doi: 10.36753/mathenot.621602 %U 10.36753/mathenot.621602 ISNAD Ci̇han, Arzu , Azak, Ayşe Zeynep , Güngör, Mehmet Ali . "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients". Mathematical Sciences and Applications E-Notes 8 / 1 (March 2020): 55-68 . https://doi.org/10.36753/mathenot.621602 AMA Ci̇han A , Azak A , Güngör M . On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Math. Sci. Appl. E-Notes. 2020; 8(1): 55-68. Vancouver Ci̇han A , Azak A , Güngör M . On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients. Mathematical Sciences and Applications E-Notes. 2020; 8(1): 55-68. IEEE A. Ci̇han , A. Azak and M. Güngör , "On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients", Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, pp. 55-68, Mar. 2020, doi:10.36753/mathenot.621602

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