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
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
Yayımlanma Tarihi
30 Haziran 2018
Gönderilme Tarihi
3 Ocak 2018
Kabul Tarihi
10 Nisan 2018
Yayımlandığı Sayı
Yıl 2018 Cilt: 2 Sayı: 1
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