Abstract
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.
References
- Abderrezzak, A., Généralisation de la transformation d'Euler d'une série formelle, Adv. Math., 103 (1994), 180--195.
- Abderrezzak1 : Abderrezzak, A., Généralisation d'identities de Carlitz, Howard et Lehmer. Aequ. Math., 49 (1995), 36--46.
- Boussayoud, A., Boughaba, S., Kerada, M., Araci, S., Acikgoz, M., Symmetric Functions of Binary Products of k-Fibonacci and Orthogonal Polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat, Ser. A Mat, RACSAM, 113 (2019), 2575-2586.
- Boussayoud, A., On some identities and generating functions for Pell-Lucas numbers, Online J. Anal. Comb., 12, (2017), 1-10.
- Boussayoud, A., Kerada, Boulyer, M. M., A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure. Appl. Math., 108, (2016), 503-511.
- Boussayoud, A., Sahali, R., The application of the operator L_{b₁b₂}^{-k} in the series ∑_{j=0}^{+∞}a_{j}b₁^{j}z^{j}, J. Adv. Res. Appl. Math., 7, (2015), 68-75. Boussayoud, A., Kerada, M., Symmetric and Generating Functions, Int. Electron. J. Pure Appl. Math., 7, (2014), 195-203.
- Boussayoud, A., L'action de l'opérateur δ_{e₁e₂}^{k}sur la série ∑_{n =0}^{+∞}S_{n}(A)e₁ⁿzⁿ, (Doctoral dissertation), Mohamed Seddik Ben Yahia University, Jijel, Algeria, (2017. Boussayoud, A., Boughaba,S., On Some Identities and Symmetric Functions for k-Pell sequences and Chebychev polynomials, Online J. Anal. Comb. 14 (2019), 1-13.
- Boussayoud, A., Kerada, M., Araci, S., Acikgoz, M., Esi, A., Generating Functions of Binary Products of Fibonacci and Tchebyshev Polynomials of first and second kinds, Filomat 33 (2019), 1495-1504.
- Djordjevic, G. B., Srivastava, H. M., Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers, Math. Comput. Modelling, 42 (2005), 1049--1056.
- Boubellouta, Kh., Boussayoud, A., Kerada, M., Symmetric Functions for Second-Order Recurrence Sequences, Tbil. Math. J., 13 (2020), 225-237.
- Boughaba, S., Boussayoud, A., Araci, S., Kerada, M., Construction of Generating Functions of Gaussian Fibonacci Numbers and Polynomials, Universal Journal of Mathematics and Applications, (Submitted).
- Jordan, J. H., Gaussian Fibonacci and Lucas numbers, Fibonacci Q., 3 (1965), 315--318.
- Asci, M., Gurel, E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes Number Theory Discrete Math., 19 (2013), 25-36.
- Halici, S., Oz, S., On Gaussian Pell Polynomials and Their Some Properties, Palest. J. Math., 7(1) (2018), 251--256.
Abstract
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.
Keywords
Symmetric functions, generating functions Gaussian Fibonacci numbers Gaussian Lucas numbers
References
- Abderrezzak, A., Généralisation de la transformation d'Euler d'une série formelle, Adv. Math., 103 (1994), 180--195.
- Abderrezzak1 : Abderrezzak, A., Généralisation d'identities de Carlitz, Howard et Lehmer. Aequ. Math., 49 (1995), 36--46.
- Boussayoud, A., Boughaba, S., Kerada, M., Araci, S., Acikgoz, M., Symmetric Functions of Binary Products of k-Fibonacci and Orthogonal Polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat, Ser. A Mat, RACSAM, 113 (2019), 2575-2586.
- Boussayoud, A., On some identities and generating functions for Pell-Lucas numbers, Online J. Anal. Comb., 12, (2017), 1-10.
- Boussayoud, A., Kerada, Boulyer, M. M., A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure. Appl. Math., 108, (2016), 503-511.
- Boussayoud, A., Sahali, R., The application of the operator L_{b₁b₂}^{-k} in the series ∑_{j=0}^{+∞}a_{j}b₁^{j}z^{j}, J. Adv. Res. Appl. Math., 7, (2015), 68-75. Boussayoud, A., Kerada, M., Symmetric and Generating Functions, Int. Electron. J. Pure Appl. Math., 7, (2014), 195-203.
- Boussayoud, A., L'action de l'opérateur δ_{e₁e₂}^{k}sur la série ∑_{n =0}^{+∞}S_{n}(A)e₁ⁿzⁿ, (Doctoral dissertation), Mohamed Seddik Ben Yahia University, Jijel, Algeria, (2017. Boussayoud, A., Boughaba,S., On Some Identities and Symmetric Functions for k-Pell sequences and Chebychev polynomials, Online J. Anal. Comb. 14 (2019), 1-13.
- Boussayoud, A., Kerada, M., Araci, S., Acikgoz, M., Esi, A., Generating Functions of Binary Products of Fibonacci and Tchebyshev Polynomials of first and second kinds, Filomat 33 (2019), 1495-1504.
- Djordjevic, G. B., Srivastava, H. M., Incomplete generalized Jacobsthal and Jacobsthal-Lucas numbers, Math. Comput. Modelling, 42 (2005), 1049--1056.
- Boubellouta, Kh., Boussayoud, A., Kerada, M., Symmetric Functions for Second-Order Recurrence Sequences, Tbil. Math. J., 13 (2020), 225-237.
- Boughaba, S., Boussayoud, A., Araci, S., Kerada, M., Construction of Generating Functions of Gaussian Fibonacci Numbers and Polynomials, Universal Journal of Mathematics and Applications, (Submitted).
- Jordan, J. H., Gaussian Fibonacci and Lucas numbers, Fibonacci Q., 3 (1965), 315--318.
- Asci, M., Gurel, E., Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes Number Theory Discrete Math., 19 (2013), 25-36.
- Halici, S., Oz, S., On Gaussian Pell Polynomials and Their Some Properties, Palest. J. Math., 7(1) (2018), 251--256.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 31, 2020 |
| Submission Date | July 29, 2019 |
| Acceptance Date | June 29, 2020 |
| Published in Issue | Year 2020 Volume: 69 Issue: 2 |
Cite
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
