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The Hyperbolic Quadrapell Sequences

Yıl 2021, Cilt: 7 Sayı: 1, 25 - 29, 30.05.2021

Öz

In this paper, we extend Quadrapell numbers to Hyperbolic Quadarapell numbers, respectively. Moreover we obtain Binet-like formulas, generating functions and some identities related with Hyperbolic Quadarpell numbers.

Kaynakça

  • ATANASSOV, K., DIMITROV, D., SHANNON, A.(2009). A remark on ψ-function and pell-padovan's sequence, Notes on Number Theory and Discrete Mathematics, 15(2), 1-44.
  • AYDIN, F.T.(2019). Hyperbolic Fibonacci sequence, Universal Journal of Mathematics and Applications, 2(2), 59-64.
  • BARREİRA, L., POPESCU, L.H., VALLS, C.(2016). Hyperbolic sequences of linear operators and evolution maps, Milan Journal of Mathematics, 84(2), 203-216.
  • BERZSENYİ, G.(1977). Gaussian fibonacci numbers
  • CATONİ, F., BOCCALETTİ, D., CANNATA, R., CATONİ, V., NİCHELATTİ, E., ZAMPETTİ, P. (2008). The mathematics of Minkowski space-time: with an introduction to commutative hypercomplex numbers, Springer Science & Business Media.
  • ÇAĞMAN, A. Repdigits as Product of Fibonacci and Pell numbers. Turkish Journal of Science, 6(1), 31-35.
  • ÇAĞMAN, A. Explicit Solutions of Powers of Three as Sums of Three Pell Numbers Based on Baker’s Type Inequalities. Turkish Journal of Inequalities, 5(1), 93-103.
  • ÇAĞMAN, A., and POLAT, K., 2021. On a Diophantine equation related to the difference of two Pell numbers. Contributions to Mathematics. Volume 3, 37-42.
  • DEVECİ, Ö., KARADUMAN, E.(2015). The pell sequences in finite groups. Util. Math, 96, 263-276.
  • DEVECİ, Ö., SHANNON, A.G.(2018). The quaternion-pell sequence. Communication in Algebra, 46(12), 50403-5409.
  • DEVECİ, Ö., SHANNON, A.G.(2020). The complex-type k- Fibonacci sequences and their applications. Communication in Algebra, pages 1-16.
  • GARGOUBI, H., KOSSENTINI, S. (2016). f-algebra structure on hyperbolic numbers, Advances in Applied Clifford Algebras, 26(4), 1211-1233.
  • GÜNCAN, A., ERBIL, Y. (2012). The q-fibonacci hyperbolic functions, In AIP Conference Proceedings, American Institute of Physics, volume 1479, pages 946-949.
  • HORADAM, A.F. (1963). Complex fibonacci numbers and fibonacci quaternions, The American Mathematical Monthly, 70(3), 289-291.
  • KHADJIEV, D., GÖKSAL, Y. (2016). Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-euclidean space, Advances in Applied Clifford Algebras, 26(2), 645-668.
  • MOTTER, A.E., ROSA, M.A.F. (2016). Hyperbolic calculus, Advances in Applied Clifford Algebras, 8(1), 109-128.
  • SHANNON, A.G., HORADAM, A.F., ANDERSON, P.G. (2006). The auxiliary equation associated with the plastic number, Notes on Number Theory and Discrete Mathematics, 12(1), 1-12.
  • SHANNON, A.G., ANDERSON, P.G., HORADAM, A.F. (2006). Properties of cordonnier, perrin and van der laan numbers, International Journal of Mathematical Education in Science and Technology, 37(7), 825-831.
  • TAS, S., DEVECI, O., KARADUMAN, E. (2014). The fibonacci-padovan sequences in fnite groups, Maejo International Journal of Science And Technology, 8(3), 279-287.
  • TAŞCI, D. (2018). Gaussian padovan and gaussian pell-padovan sequences, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2), 82-88.
  • VOET, C. (2012). The poetics of order: Dom hans van der laan's architectonic space, Architectural Research Quarterly, 16(2), 137.
Yıl 2021, Cilt: 7 Sayı: 1, 25 - 29, 30.05.2021

Öz

Kaynakça

  • ATANASSOV, K., DIMITROV, D., SHANNON, A.(2009). A remark on ψ-function and pell-padovan's sequence, Notes on Number Theory and Discrete Mathematics, 15(2), 1-44.
  • AYDIN, F.T.(2019). Hyperbolic Fibonacci sequence, Universal Journal of Mathematics and Applications, 2(2), 59-64.
  • BARREİRA, L., POPESCU, L.H., VALLS, C.(2016). Hyperbolic sequences of linear operators and evolution maps, Milan Journal of Mathematics, 84(2), 203-216.
  • BERZSENYİ, G.(1977). Gaussian fibonacci numbers
  • CATONİ, F., BOCCALETTİ, D., CANNATA, R., CATONİ, V., NİCHELATTİ, E., ZAMPETTİ, P. (2008). The mathematics of Minkowski space-time: with an introduction to commutative hypercomplex numbers, Springer Science & Business Media.
  • ÇAĞMAN, A. Repdigits as Product of Fibonacci and Pell numbers. Turkish Journal of Science, 6(1), 31-35.
  • ÇAĞMAN, A. Explicit Solutions of Powers of Three as Sums of Three Pell Numbers Based on Baker’s Type Inequalities. Turkish Journal of Inequalities, 5(1), 93-103.
  • ÇAĞMAN, A., and POLAT, K., 2021. On a Diophantine equation related to the difference of two Pell numbers. Contributions to Mathematics. Volume 3, 37-42.
  • DEVECİ, Ö., KARADUMAN, E.(2015). The pell sequences in finite groups. Util. Math, 96, 263-276.
  • DEVECİ, Ö., SHANNON, A.G.(2018). The quaternion-pell sequence. Communication in Algebra, 46(12), 50403-5409.
  • DEVECİ, Ö., SHANNON, A.G.(2020). The complex-type k- Fibonacci sequences and their applications. Communication in Algebra, pages 1-16.
  • GARGOUBI, H., KOSSENTINI, S. (2016). f-algebra structure on hyperbolic numbers, Advances in Applied Clifford Algebras, 26(4), 1211-1233.
  • GÜNCAN, A., ERBIL, Y. (2012). The q-fibonacci hyperbolic functions, In AIP Conference Proceedings, American Institute of Physics, volume 1479, pages 946-949.
  • HORADAM, A.F. (1963). Complex fibonacci numbers and fibonacci quaternions, The American Mathematical Monthly, 70(3), 289-291.
  • KHADJIEV, D., GÖKSAL, Y. (2016). Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-euclidean space, Advances in Applied Clifford Algebras, 26(2), 645-668.
  • MOTTER, A.E., ROSA, M.A.F. (2016). Hyperbolic calculus, Advances in Applied Clifford Algebras, 8(1), 109-128.
  • SHANNON, A.G., HORADAM, A.F., ANDERSON, P.G. (2006). The auxiliary equation associated with the plastic number, Notes on Number Theory and Discrete Mathematics, 12(1), 1-12.
  • SHANNON, A.G., ANDERSON, P.G., HORADAM, A.F. (2006). Properties of cordonnier, perrin and van der laan numbers, International Journal of Mathematical Education in Science and Technology, 37(7), 825-831.
  • TAS, S., DEVECI, O., KARADUMAN, E. (2014). The fibonacci-padovan sequences in fnite groups, Maejo International Journal of Science And Technology, 8(3), 279-287.
  • TAŞCI, D. (2018). Gaussian padovan and gaussian pell-padovan sequences, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(2), 82-88.
  • VOET, C. (2012). The poetics of order: Dom hans van der laan's architectonic space, Architectural Research Quarterly, 16(2), 137.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Sait Taş

Yayımlanma Tarihi 30 Mayıs 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 7 Sayı: 1

Kaynak Göster

APA Taş, S. (2021). The Hyperbolic Quadrapell Sequences. Eastern Anatolian Journal of Science, 7(1), 25-29.
AMA Taş S. The Hyperbolic Quadrapell Sequences. Eastern Anatolian Journal of Science. Mayıs 2021;7(1):25-29.
Chicago Taş, Sait. “The Hyperbolic Quadrapell Sequences”. Eastern Anatolian Journal of Science 7, sy. 1 (Mayıs 2021): 25-29.
EndNote Taş S (01 Mayıs 2021) The Hyperbolic Quadrapell Sequences. Eastern Anatolian Journal of Science 7 1 25–29.
IEEE S. Taş, “The Hyperbolic Quadrapell Sequences”, Eastern Anatolian Journal of Science, c. 7, sy. 1, ss. 25–29, 2021.
ISNAD Taş, Sait. “The Hyperbolic Quadrapell Sequences”. Eastern Anatolian Journal of Science 7/1 (Mayıs 2021), 25-29.
JAMA Taş S. The Hyperbolic Quadrapell Sequences. Eastern Anatolian Journal of Science. 2021;7:25–29.
MLA Taş, Sait. “The Hyperbolic Quadrapell Sequences”. Eastern Anatolian Journal of Science, c. 7, sy. 1, 2021, ss. 25-29.
Vancouver Taş S. The Hyperbolic Quadrapell Sequences. Eastern Anatolian Journal of Science. 2021;7(1):25-9.