In this paper, we introduce a operator in order to derive some new symmetric properties of Gaussian Fibonacci numbers and Gaussian Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions for Gaussian Fibonacci numbers and Gaussian Jacobsthal polynomials. In the paper Al4, Al5, a second-order linear recurrence sequence (U_{n}(a,b;p,q))_{n≥0} or briefly (U_{n})_{n≥0} is considered by the recurrence relation:
U_{n+2}=pU_{n+1}+qU_{n},
with the initial conditions U₀=a and U₁=b, where a,b∈ℂ and p,q∈ℤ₊ for n≥0.
In this paper, we introduce a operator in order to derive some new symmetric properties of Gaussian Fibonacci numbers and Gaussian Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions for Gaussian Fibonacci numbers and Gaussian Jacobsthal polynomials. In the paper Al4, Al5, a second-order linear recurrence sequence (U_{n}(a,b;p,q))_{n≥0} or briefly (U_{n})_{n≥0} is considered by the recurrence relation:
U_{n+2}=pU_{n+1}+qU_{n},
with the initial conditions U₀=a and U₁=b, where a,b∈ℂ and p,q∈ℤ₊ for n≥0.
Symmetric functions, generating functions Gaussian Fibonacci numbers Gaussian Lucas numbers
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 31 Aralık 2020 |
Gönderilme Tarihi | 29 Temmuz 2019 |
Kabul Tarihi | 29 Haziran 2020 |
Yayımlandığı Sayı | Yıl 2020 Cilt: 69 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
This work is licensed under a Creative Commons Attribution 4.0 International License.