Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 5 Sayı: 4, 145 - 155, 29.12.2022
https://doi.org/10.32323/ujma.1207852

Öz

Kaynakça

  • [1] P. Ribenboim. My Numbers, My Friends, Popular Lectures on Number Theory. Springer-Verlag, New York, Inc. 2000.
  • [2] A. Özkoc¸, Some algebraic identities on quadra Fibona-Pell integer sequence, Adv. Differ. Equ., 2015 (2015), Article Number: 148, 10 pages.
  • [3] C. Kızılates¸, On the quadra Lucas-Jacobsthal numbers, Karaelmas Sci. Eng. J., 7(2) (2017), 619-621.
  • [4] O. Dişkaya, H. Menken, On the quadra Fibona-Pell and hexa-Fibona-Pell-Jacobsthal sequences, Mathematical Sciences and Applications E-notes, 7(2) (2019), 149-160.
  • [5] A. Tekcan, A. Özkoc¸, M. Engür, M. E. Özbek, On algebraic identities on a new integer sequence with four parameters, Ars Comb., 127 (2016), 225-238.
  • [6] W. R. Hamilton, Elements of Quaternions, London, England, Green Company, 1866.
  • [7] M. N. S. Swamy, On generalized Fibonacci quaternions, Fibonacci Q., 5 (1973), 547-550.
  • [8] A. F. Horadam, Quaternion recurrence relations, Ulam Q., 2(2) (1993), 22-33.
  • [9] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison Wesley Publishing Company, 1998.
  • [10] K. W. Chen, Identities from the Binomial Transform, J. Number Theory, 124, 142-150, 2007.
  • [11] S. Falcon, A. Plaza, Binomial Transforms of the k􀀀Fibonacci Sequences, Int. J. Nonlinear Sci. Numer. Simul., 10, 1305-1316, 2009.
  • [12] H. Prodinger, Some Information about the Binomial Transform, The Fibonacci Q., 32 (5), 412-415, 1994.
  • [13] H. W. Gould, Series Transformations for Findings Recurrences for Sequences, The Fibonacci Q., 28(2), 166-171, 1990.
  • [14] S. Falcon, Binomial Transform of the Generalized k􀀀Fibonacci Numbers, Commun. Math. Anal., Vol. 10, No. 3, pp. 643–651, 2019
  • [15] C. Kızılates¸, N. Tuğlu, B. Çekim, Binomial transform of quadrapell sequences and quadrapell matrix sequences, J. Sci. Arts, 1(38) (2017), 69-80.
  • [16] T. C¸ etinalp, Kuadra Fibona-Pell kuaterniyon dizileri ¨¨uzerine bazı cebirsel ¨ozdes¸likler, MSc. Thesis, Karamano˘glu Mehmetbey University, 2017.
  • [17] F. Kaplan, A. Özkoc¸ Öztürk, On the binomial transforms of the Horadam quaternion sequences, Math. Meth. Appl. Sci., 45 (2022), 12009-12022.
  • [18] E. Polatlı, On certain properties of quadrapell sequences, Karaelmas Sci. Eng. J., 8(1) (2018), 305-308.

Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion

Yıl 2022, Cilt: 5 Sayı: 4, 145 - 155, 29.12.2022
https://doi.org/10.32323/ujma.1207852

Öz

The main object of the study is to consider the binomial transform for quadra Fibona-Pell sequence and quadra Fibona-Pell quaternion. In the paper, which consists of two parts in terms of the results found, the first step was taken for the sequence by defining the binomial transform for the quadra Fibona-Pell sequence in the first part and then finding the recurrence relation of this new binomial transform. Then, the Binet formula, generating function and various sum formulas of the sequence were found. In the second part, the binomial transform is applied for the quadra Fibona-Pell quaternion, which was discussed in a thesis before. Similar results in the first section are covered in the quaternion binomial transform.

Kaynakça

  • [1] P. Ribenboim. My Numbers, My Friends, Popular Lectures on Number Theory. Springer-Verlag, New York, Inc. 2000.
  • [2] A. Özkoc¸, Some algebraic identities on quadra Fibona-Pell integer sequence, Adv. Differ. Equ., 2015 (2015), Article Number: 148, 10 pages.
  • [3] C. Kızılates¸, On the quadra Lucas-Jacobsthal numbers, Karaelmas Sci. Eng. J., 7(2) (2017), 619-621.
  • [4] O. Dişkaya, H. Menken, On the quadra Fibona-Pell and hexa-Fibona-Pell-Jacobsthal sequences, Mathematical Sciences and Applications E-notes, 7(2) (2019), 149-160.
  • [5] A. Tekcan, A. Özkoc¸, M. Engür, M. E. Özbek, On algebraic identities on a new integer sequence with four parameters, Ars Comb., 127 (2016), 225-238.
  • [6] W. R. Hamilton, Elements of Quaternions, London, England, Green Company, 1866.
  • [7] M. N. S. Swamy, On generalized Fibonacci quaternions, Fibonacci Q., 5 (1973), 547-550.
  • [8] A. F. Horadam, Quaternion recurrence relations, Ulam Q., 2(2) (1993), 22-33.
  • [9] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison Wesley Publishing Company, 1998.
  • [10] K. W. Chen, Identities from the Binomial Transform, J. Number Theory, 124, 142-150, 2007.
  • [11] S. Falcon, A. Plaza, Binomial Transforms of the k􀀀Fibonacci Sequences, Int. J. Nonlinear Sci. Numer. Simul., 10, 1305-1316, 2009.
  • [12] H. Prodinger, Some Information about the Binomial Transform, The Fibonacci Q., 32 (5), 412-415, 1994.
  • [13] H. W. Gould, Series Transformations for Findings Recurrences for Sequences, The Fibonacci Q., 28(2), 166-171, 1990.
  • [14] S. Falcon, Binomial Transform of the Generalized k􀀀Fibonacci Numbers, Commun. Math. Anal., Vol. 10, No. 3, pp. 643–651, 2019
  • [15] C. Kızılates¸, N. Tuğlu, B. Çekim, Binomial transform of quadrapell sequences and quadrapell matrix sequences, J. Sci. Arts, 1(38) (2017), 69-80.
  • [16] T. C¸ etinalp, Kuadra Fibona-Pell kuaterniyon dizileri ¨¨uzerine bazı cebirsel ¨ozdes¸likler, MSc. Thesis, Karamano˘glu Mehmetbey University, 2017.
  • [17] F. Kaplan, A. Özkoc¸ Öztürk, On the binomial transforms of the Horadam quaternion sequences, Math. Meth. Appl. Sci., 45 (2022), 12009-12022.
  • [18] E. Polatlı, On certain properties of quadrapell sequences, Karaelmas Sci. Eng. J., 8(1) (2018), 305-308.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Arzu Özkoç

Eda Gündüz Bu kişi benim 0000-0003-1985-6506

Yayımlanma Tarihi 29 Aralık 2022
Gönderilme Tarihi 21 Kasım 2022
Kabul Tarihi 26 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 4

Kaynak Göster

APA Özkoç, A., & Gündüz, E. (2022). Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion. Universal Journal of Mathematics and Applications, 5(4), 145-155. https://doi.org/10.32323/ujma.1207852
AMA Özkoç A, Gündüz E. Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion. Univ. J. Math. Appl. Aralık 2022;5(4):145-155. doi:10.32323/ujma.1207852
Chicago Özkoç, Arzu, ve Eda Gündüz. “Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion”. Universal Journal of Mathematics and Applications 5, sy. 4 (Aralık 2022): 145-55. https://doi.org/10.32323/ujma.1207852.
EndNote Özkoç A, Gündüz E (01 Aralık 2022) Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion. Universal Journal of Mathematics and Applications 5 4 145–155.
IEEE A. Özkoç ve E. Gündüz, “Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion”, Univ. J. Math. Appl., c. 5, sy. 4, ss. 145–155, 2022, doi: 10.32323/ujma.1207852.
ISNAD Özkoç, Arzu - Gündüz, Eda. “Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion”. Universal Journal of Mathematics and Applications 5/4 (Aralık 2022), 145-155. https://doi.org/10.32323/ujma.1207852.
JAMA Özkoç A, Gündüz E. Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion. Univ. J. Math. Appl. 2022;5:145–155.
MLA Özkoç, Arzu ve Eda Gündüz. “Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion”. Universal Journal of Mathematics and Applications, c. 5, sy. 4, 2022, ss. 145-5, doi:10.32323/ujma.1207852.
Vancouver Özkoç A, Gündüz E. Binomial Transform for Quadra Fibona-Pell Sequence and Quadra Fibona-Pell Quaternion. Univ. J. Math. Appl. 2022;5(4):145-5.

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