Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence

Tulay Yagmur; Nusret Karaaslan

doi:10.29002/asujse.374128

Research Article

Year 2018, , 63 - 72, 30.06.2018

Tulay Yagmur , Nusret Karaaslan

https://doi.org/10.29002/asujse.374128

Cited By: 6

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, , 63 - 72, 30.06.2018

Tulay Yagmur , Nusret Karaaslan

https://doi.org/10.29002/asujse.374128

Cited By: 6

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.

Keywords

Modified Pell sequence, Modified Pell polynomial sequence, Gaussian modified Pell sequence, 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 2018

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