Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence

Tulay Yagmur; Nusret Karaaslan

doi:10.29002/asujse.374128

EN

Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence

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.
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[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.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Tulay Yagmur ^*
AKSARAY ÜNİVERSİTESİ
Türkiye

Nusret Karaaslan
AKSARAY ÜNİVERSİTESİ
Türkiye

Publication Date

June 30, 2018

Submission Date

January 3, 2018

Acceptance Date

April 10, 2018

Published in Issue

Year 2018 Volume: 2 Number: 1

DOI

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

IZ

https://izlik.org/JA83FA57SN

Cite

RIS / Bibtex

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