Gaussian Modified Pell Sequence and Gaussian Modified Pell Polynomial Sequence

Tulay Yagmur; Nusret Karaaslan

doi:10.29002/asujse.374128

Araştırma Makalesi

Yıl 2018, , 63 - 72, 30.06.2018

Tulay Yagmur , Nusret Karaaslan

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

Cited By: 6

Öz

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.
[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

Yıl 2018, , 63 - 72, 30.06.2018

Tulay Yagmur , Nusret Karaaslan

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

Cited By: 6

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.
[9] S. Halıcı, S. Öz, On Gaussian Pell Polynomials and Their Some Properties. Palestine Journal of Mathematics 7(1) (2018) 251-256.

Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Mühendislik
Bölüm	Araştırma Makalesi
Yazarlar	Tulay Yagmur Nusret Karaaslan
Yayımlanma Tarihi	30 Haziran 2018
Gönderilme Tarihi	3 Ocak 2018
Kabul Tarihi	10 Nisan 2018
Yayımlandığı Sayı	Yıl 2018

Kaynak Göster

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