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BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 69 Sayı: 1, 880 - 890, 30.06.2020

Tülay Yağmur

https://doi.org/10.31801/cfsuasmas.582674
Cited By: 1

Öz

Kaynakça

  • Adler, S. L., Quaternionic quantum mechanics and quantum fields, 88. Oxford Univ. Press on Demand, 1995.
  • Akyigit, M., Kosal, H. H. and Tosun, M., Split Fibonacci quaternions, Adv. Appl. Clifford Algebras 23 (2013), 535-545.
  • Aydin, F. T., The k-Fibonacci dual quaternions, Int. J. Mathematical Analysis 12 (2018), 363-373.
  • Aydin, F. T., Bicomplex Fibonacci quaternions, Chaos Solitons Fractals 106 (2018), 147-153.
  • Aydin, F. T., Hyperbolic k-Fibonacci quaternions, arXiv:1812.00781v1, 2018.
  • Bilgici, G., Tokeser, U. and Unal, Z., k- Fibonacci and k-Lucas generalized quaternions, Konuralp J. Math. 5 (2017), 102-113.
  • Catarino, P., On some identities and generating functions for k-Pell numbers, Int. J. Mathematical Analysis 7 (2013), 1877-1884.
  • Ell, T. A., Bihan, N. L. and Sangwine, S. J., Quaternion Fourier transforms for signal and image processing, John Wiley and Sons, 2014.
  • Falcon, S. and Plaza, A., On the Fibonacci k-numbers, Chaos Solitons Fractals 32 (2007), 1615-1624.
  • Finkelstein, D., Jauch, J. M., Schiminovich, S. and Speiser, D., Foundations of quaternion quantum mechanics, J. Math. Phys. 3 (1962), 207-220.
  • Girard, P. R., The quaternion group and modern physics, Eur. J. Phys. 5 (1984), 25-32.
  • Halici, S., On Fibonacci quaternions, Adv. Appl. Clifford Algebras 22 (2012), 321-327.
  • Halici, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras 23 (2013), 105-112.
  • Hamilton, W. R., Lectures on quaternions, Hodges and Smith, Dublin, 1853.
  • Horadam, A. F., A generalized Fibonacci sequence, The American Math. Monthly 68 (1961), 455-459.
  • Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, The American Math. Monthly 70 (1963), 289-291.
  • Horadam, A. F., Basic properties of a certain generalized sequence of numbers, The Fibonacci Quart. 3 (1965), 161-176.
  • Horadam, A. F., Pell identities, The Fibonacci Quart. 9 (1971), 245-252.
  • Horadam, A. F., Jacobsthal representation numbers, The Fibonacci Quart. 34 (1996), 40-54.
  • Ipek, A., On (p,q)-Fibonacci quaternions and their Binet formulas, generating functions and certain binomial sums, Adv. Appl. Clifford Algebras 27 (2017), 1343-1351.
  • Iyer, M. R., A note on Fibonacci quaternions, The Fibonacci Quart. 7 (1969), 225-229.
  • Jhala, D., Sisodiya, K. and Rathore, G. P. S., On some identities for k-Jacobsthal numbers, Int. J. Mathematical Analysis 7 (2013), 551-556.
  • Kosal, I. A., A note on hyperbolic quaternions, Universal Journal of Mathematics and Applications 1 (2018), 155-159.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, New York, 2001.
  • Mac-Farlane, A., Hyperbolic quaternions, Proc. Roy. Soc. Edinburg 23 (1902), 169-180.
  • Patel, B. K. and Ray, P. K., On the properties of (p,q)-Fibonacci and (p,q)-Lucas quaternions, Mathematical Reports 21 (2019), 15-25.
  • Polatli, E., Kizilates, C. and Kesim, S., On split k-Fibonacci and k-Lucas quaternions, Adv. Appl. Clifford Algebras 26 (2016), 353-362.
  • Ramirez, J. L., Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta 23 (2015), 201-212.
  • Ribenboim, P., My Numbers, My Friends: Popular Lectures on Number Theory, Springer-Verlag, New York, 2000.
  • Senturk, T. D., Dasdemir, A., Bilgici, G. and Unal, Z., On unrestricted Horadam generalized quaternions, Utilitas Mathematica 110 (2019), 89-98.
  • Tan, E., Yilmaz, S. and Sahin, M., On a new generalization of Fibonacci quaternions, Chaos Solitons Fractals 82 (2016), 1-4.
  • Ward, J. P., Quaternions and Cayley Numbers: Algebra and Applications, Kluwer, London, 1997.

A note on hyperbolic (p,q)-Fibonacci quaternions

Yıl 2020, Cilt: 69 Sayı: 1, 880 - 890, 30.06.2020

Tülay Yağmur

https://doi.org/10.31801/cfsuasmas.582674
Cited By: 1

Öz

In this paper, we introduce a new quaternion sequence called  hyperbolic (p,q)-Fibonacci  quaternions.  This new quaternion sequence includes hyperbolic Fibonacci, hyperbolic k-Fibonacci, hyperbolic  Pell, hyperbolic k-Pell, hyperbolic  Jacobsthal, hyperbolic k-Jacobsthal quaternions. We give generating function and Binet formula for these quaternions. We also obtain   some  identities such as d'Ocagne's, Catalan's and Cassini's identities involving  hyperbolic (p,q)-Fibonacci  quaternions.

Anahtar Kelimeler

Fibonacci numbers (p;q)-Fibonacci numbers (p;q)-Fibonacci quaternions hyperbolic quaternions hyperbolic (p;q)-Fibonacci quaternions

Kaynakça

  • Adler, S. L., Quaternionic quantum mechanics and quantum fields, 88. Oxford Univ. Press on Demand, 1995.
  • Akyigit, M., Kosal, H. H. and Tosun, M., Split Fibonacci quaternions, Adv. Appl. Clifford Algebras 23 (2013), 535-545.
  • Aydin, F. T., The k-Fibonacci dual quaternions, Int. J. Mathematical Analysis 12 (2018), 363-373.
  • Aydin, F. T., Bicomplex Fibonacci quaternions, Chaos Solitons Fractals 106 (2018), 147-153.
  • Aydin, F. T., Hyperbolic k-Fibonacci quaternions, arXiv:1812.00781v1, 2018.
  • Bilgici, G., Tokeser, U. and Unal, Z., k- Fibonacci and k-Lucas generalized quaternions, Konuralp J. Math. 5 (2017), 102-113.
  • Catarino, P., On some identities and generating functions for k-Pell numbers, Int. J. Mathematical Analysis 7 (2013), 1877-1884.
  • Ell, T. A., Bihan, N. L. and Sangwine, S. J., Quaternion Fourier transforms for signal and image processing, John Wiley and Sons, 2014.
  • Falcon, S. and Plaza, A., On the Fibonacci k-numbers, Chaos Solitons Fractals 32 (2007), 1615-1624.
  • Finkelstein, D., Jauch, J. M., Schiminovich, S. and Speiser, D., Foundations of quaternion quantum mechanics, J. Math. Phys. 3 (1962), 207-220.
  • Girard, P. R., The quaternion group and modern physics, Eur. J. Phys. 5 (1984), 25-32.
  • Halici, S., On Fibonacci quaternions, Adv. Appl. Clifford Algebras 22 (2012), 321-327.
  • Halici, S., On complex Fibonacci quaternions, Adv. Appl. Clifford Algebras 23 (2013), 105-112.
  • Hamilton, W. R., Lectures on quaternions, Hodges and Smith, Dublin, 1853.
  • Horadam, A. F., A generalized Fibonacci sequence, The American Math. Monthly 68 (1961), 455-459.
  • Horadam, A. F., Complex Fibonacci numbers and Fibonacci quaternions, The American Math. Monthly 70 (1963), 289-291.
  • Horadam, A. F., Basic properties of a certain generalized sequence of numbers, The Fibonacci Quart. 3 (1965), 161-176.
  • Horadam, A. F., Pell identities, The Fibonacci Quart. 9 (1971), 245-252.
  • Horadam, A. F., Jacobsthal representation numbers, The Fibonacci Quart. 34 (1996), 40-54.
  • Ipek, A., On (p,q)-Fibonacci quaternions and their Binet formulas, generating functions and certain binomial sums, Adv. Appl. Clifford Algebras 27 (2017), 1343-1351.
  • Iyer, M. R., A note on Fibonacci quaternions, The Fibonacci Quart. 7 (1969), 225-229.
  • Jhala, D., Sisodiya, K. and Rathore, G. P. S., On some identities for k-Jacobsthal numbers, Int. J. Mathematical Analysis 7 (2013), 551-556.
  • Kosal, I. A., A note on hyperbolic quaternions, Universal Journal of Mathematics and Applications 1 (2018), 155-159.
  • Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, New York, 2001.
  • Mac-Farlane, A., Hyperbolic quaternions, Proc. Roy. Soc. Edinburg 23 (1902), 169-180.
  • Patel, B. K. and Ray, P. K., On the properties of (p,q)-Fibonacci and (p,q)-Lucas quaternions, Mathematical Reports 21 (2019), 15-25.
  • Polatli, E., Kizilates, C. and Kesim, S., On split k-Fibonacci and k-Lucas quaternions, Adv. Appl. Clifford Algebras 26 (2016), 353-362.
  • Ramirez, J. L., Some combinatorial properties of the k-Fibonacci and the k-Lucas quaternions, An. St. Univ. Ovidius Constanta 23 (2015), 201-212.
  • Ribenboim, P., My Numbers, My Friends: Popular Lectures on Number Theory, Springer-Verlag, New York, 2000.
  • Senturk, T. D., Dasdemir, A., Bilgici, G. and Unal, Z., On unrestricted Horadam generalized quaternions, Utilitas Mathematica 110 (2019), 89-98.
  • Tan, E., Yilmaz, S. and Sahin, M., On a new generalization of Fibonacci quaternions, Chaos Solitons Fractals 82 (2016), 1-4.
  • Ward, J. P., Quaternions and Cayley Numbers: Algebra and Applications, Kluwer, London, 1997.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Tülay Yağmur 0000-0002-6224-1921

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 26 Haziran 2019
Kabul Tarihi 24 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Yağmur, T. (2020). A note on hyperbolic (p,q)-Fibonacci quaternions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 880-890. https://doi.org/10.31801/cfsuasmas.582674
AMA Yağmur T. A note on hyperbolic (p,q)-Fibonacci quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):880-890. doi:10.31801/cfsuasmas.582674
Chicago Yağmur, Tülay. “A Note on Hyperbolic (p,q)-Fibonacci Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 880-90. https://doi.org/10.31801/cfsuasmas.582674.
EndNote Yağmur T (01 Haziran 2020) A note on hyperbolic (p,q)-Fibonacci quaternions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 880–890.
IEEE T. Yağmur, “A note on hyperbolic (p,q)-Fibonacci quaternions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 880–890, 2020, doi: 10.31801/cfsuasmas.582674.
ISNAD Yağmur, Tülay. “A Note on Hyperbolic (p,q)-Fibonacci Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 880-890. https://doi.org/10.31801/cfsuasmas.582674.
JAMA Yağmur T. A note on hyperbolic (p,q)-Fibonacci quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:880–890.
MLA Yağmur, Tülay. “A Note on Hyperbolic (p,q)-Fibonacci Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 880-9, doi:10.31801/cfsuasmas.582674.
Vancouver Yağmur T. A note on hyperbolic (p,q)-Fibonacci quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):880-9.

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https://doi.org/10.53570/jnt.1199465

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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