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

Year 2020, , 55 - 68, 20.03.2020
https://doi.org/10.36753/mathenot.621602

Abstract

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].

References

  • [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).
Year 2020, , 55 - 68, 20.03.2020
https://doi.org/10.36753/mathenot.621602

Abstract

References

  • [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).
There are 11 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Arzu Cihan This is me

Ayşe Zeynep Azak

Mehmet Ali Güngör 0000-0003-1863-3183

Publication Date March 20, 2020
Submission Date September 18, 2019
Acceptance Date February 14, 2020
Published in Issue Year 2020

Cite

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. March 2020;8(1):55-68. doi:10.36753/mathenot.621602
Chicago Cihan, Arzu, Ayşe Zeynep Azak, and Mehmet Ali Güngör. “On Dual-Complex Numbers With Generalized Fibonacci and Lucas Numbers Coefficients”. Mathematical Sciences and Applications E-Notes 8, no. 1 (March 2020): 55-68. https://doi.org/10.36753/mathenot.621602.
EndNote Cihan A, Azak AZ, Güngör MA (March 1, 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, and M. A. Güngör, “On Dual-Complex Numbers with Generalized Fibonacci and Lucas Numbers Coefficients”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 55–68, 2020, doi: 10.36753/mathenot.621602.
ISNAD Cihan, Arzu et al. “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.
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 et al. “On Dual-Complex Numbers With Generalized Fibonacci and Lucas Numbers Coefficients”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, 2020, pp. 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.

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