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Year 2018, Volume: 2 Issue: 1, 63 - 72, 30.06.2018
https://doi.org/10.29002/asujse.374128

Abstract

References

  • [1] A.F. Horadam, Complex Fibonacci Numbers and Fibonacci Quaternions. American Math. Monthly 70 (1963) 289-291.
  • [2] G. Berzsenyi, Gaussian Fibonacci Numbers. Fibonacci Quarterly 15(3) (1977) 233-236.
  • [3] J.H. Jordan, Gaussian Fibonacci and Lucas Numbers. Fibonacci Quarterly 3 (1965) 315-318.
  • [4] J.J. Good, Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio. Fibonacci Quaterly 31(1) (1981) 7-20.
  • [5] C.J. Harman, Complex Fibonacci Numbers. Fibonacci Quaterly 19(1) (1981) 82-86.
  • [6] S. Pethe, A.F. Horadam, Generalized Gaussian Fibonacci Numbers. Bull. Austral. Math. Soc. 33(1) (1986) 37-48.
  • [7] S. Halıcı, S. Öz, On Some Gaussian Pell and Pell-Lucas Numbers. Ordu Univ. Science and Technology Journal 6(1) (2016) 8-18.
  • [8] A. F. Horadam, J. M. Mahon, Pell and Pell-Lucas polynomials. Fibonacci Quarterly 23(1) (1985) 7-20.
  • [9] S. Halıcı, S. Öz, On Gaussian Pell Polynomials and Their Some Properties. Palestine Journal of Mathematics 7(1) (2018) 251-256.

Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence

Year 2018, Volume: 2 Issue: 1, 63 - 72, 30.06.2018
https://doi.org/10.29002/asujse.374128

Abstract

In this
paper, we first define the Gaussian modified Pell sequence
, for n ≥ 2, by the relation  = 2 +  with initial conditions  = 1 ─ i and  = 1 + i. Then
we give the definition of
the
Gaussian modified Pell polynomial sequence
, for n ≥ 2, by the relation  = 2 +  with initial conditions  = 1─ xi and  = x + i. We
give Binet’s formulas, generating functions and summation formulas of these sequences.
We also obtain some well-known identities such as Catalan’s identities,
Cassini’s identities and
d’Ocagne’s
identities
involving the
Gaussian modified Pell sequence and Gaussian modified Pell polynomial sequence.

References

  • [1] A.F. Horadam, Complex Fibonacci Numbers and Fibonacci Quaternions. American Math. Monthly 70 (1963) 289-291.
  • [2] G. Berzsenyi, Gaussian Fibonacci Numbers. Fibonacci Quarterly 15(3) (1977) 233-236.
  • [3] J.H. Jordan, Gaussian Fibonacci and Lucas Numbers. Fibonacci Quarterly 3 (1965) 315-318.
  • [4] J.J. Good, Complex Fibonacci and Lucas Numbers, Continued Fractions, and the Square Root of the Golden Ratio. Fibonacci Quaterly 31(1) (1981) 7-20.
  • [5] C.J. Harman, Complex Fibonacci Numbers. Fibonacci Quaterly 19(1) (1981) 82-86.
  • [6] S. Pethe, A.F. Horadam, Generalized Gaussian Fibonacci Numbers. Bull. Austral. Math. Soc. 33(1) (1986) 37-48.
  • [7] S. Halıcı, S. Öz, On Some Gaussian Pell and Pell-Lucas Numbers. Ordu Univ. Science and Technology Journal 6(1) (2016) 8-18.
  • [8] A. F. Horadam, J. M. Mahon, Pell and Pell-Lucas polynomials. Fibonacci Quarterly 23(1) (1985) 7-20.
  • [9] S. Halıcı, S. Öz, On Gaussian Pell Polynomials and Their Some Properties. Palestine Journal of Mathematics 7(1) (2018) 251-256.
There are 9 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Tulay Yagmur

Nusret Karaaslan

Publication Date June 30, 2018
Submission Date January 3, 2018
Acceptance Date April 10, 2018
Published in Issue Year 2018Volume: 2 Issue: 1

Cite

APA Yagmur, T., & Karaaslan, N. (2018). Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence. Aksaray University Journal of Science and Engineering, 2(1), 63-72. https://doi.org/10.29002/asujse.374128

Aksaray J. Sci. Eng. | e-ISSN: 2587-1277 | Period: Biannually | Founded: 2017 | Publisher: Aksaray University | https://asujse.aksaray.edu.tr




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