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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

[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.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Mühendislik

Bölüm

Araştırma Makalesi

Yazarlar

Tulay Yagmur ^*
AKSARAY ÜNİVERSİTESİ
Türkiye

Nusret Karaaslan
AKSARAY ÜNİVERSİTESİ
Türkiye

Yayımlanma Tarihi

30 Haziran 2018

Gönderilme Tarihi

3 Ocak 2018

Kabul Tarihi

10 Nisan 2018

Yayımlandığı Sayı

Yıl 2018 Cilt: 2 Sayı: 1

DOI

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

IZ

https://izlik.org/JA83FA57SN

Kaynak Göster

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

AMA

1.Yagmur T, Karaaslan N. Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence. Aksaray J. Sci. Eng. 2018;2(1):63-72. doi:10.29002/asujse.374128

Chicago

Yagmur, Tulay, ve Nusret Karaaslan. 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.

EndNote

Yagmur T, Karaaslan N (01 Haziran 2018) Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence. Aksaray University Journal of Science and Engineering 2 1 63–72.

IEEE

[1]T. Yagmur ve N. Karaaslan, “Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence”, Aksaray J. Sci. Eng., c. 2, sy 1, ss. 63–72, Haz. 2018, doi: 10.29002/asujse.374128.

ISNAD

Yagmur, Tulay - Karaaslan, Nusret. “Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence”. Aksaray University Journal of Science and Engineering 2/1 (01 Haziran 2018): 63-72. https://doi.org/10.29002/asujse.374128.

JAMA

1.Yagmur T, Karaaslan N. Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence. Aksaray J. Sci. Eng. 2018;2:63–72.

MLA

Yagmur, Tulay, ve Nusret Karaaslan. “Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence”. Aksaray University Journal of Science and Engineering, c. 2, sy 1, Haziran 2018, ss. 63-72, doi:10.29002/asujse.374128.

Vancouver

1.Tulay Yagmur, Nusret Karaaslan. Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence. Aksaray J. Sci. Eng. 01 Haziran 2018;2(1):63-72. doi:10.29002/asujse.374128