On Some Identities And Generating Function of Both K-jacobsthal Numbers and Symmetric Functions in Several Variables

Yıl 2019, Cilt: 7 Sayı: 2, 235 - 242, 15.10.2019

Souhila Boughaba Ali Boussayoud

Öz

In this paper, we derive new generating functions for the products of $k$-Fibonacci numbers at negative indices, $k$-Pell numbers at negative indices, $k$-Jacobsthal numbers at negative indices, the\ product of $k$-Fibonacci numbers and Tribonacci numbers, Jacobsthal polynomials and symmetric functions in several variables by making use of useful properties of the symmetric functions.

Anahtar Kelimeler

k-Fibonacci numbers; Generating functions; k-Pell numbers.

Kaynakça

• [1] A. Boussayoud, S. Boughaba, M. Kerada, S. Araci and M. Acikgoz, Generating functions of binary products of k-Fibonacci and orthogonal polynomials, Rev. R. Acad. Cienc. Exactas F´ıs. Nat., Ser. A Mat. 113, (2019), 2575-2586.
• [2] A. Boussayoud, S. Boughaba, On Some Identities and Generating Functions for k-Pell sequences and Chebyshev polynomials, Online J. Anal. Comb. 14 #3, (2019), 1-13.
• [3] A. Boussayoud and A. Abderrezzak, Complete Homogeneous Symmetric Functions and Hadamard Product, Ars Comb. 144, (2019), 81-90.
• [4] A. Boussayoud, A. Abderrezzak and S. Araci, A new symmetric endomorphism operator for some generalizations of certain generating functions, Notes Number Theory Discrete Math.24, (2018), 45-58, .
• [5] A. Boussayoud, M. Kerada, N. Harrouche, On the k-Lucas numbers and Lucas Polynomials, Turkish Journal of Analysis and Number.5(3), (2017), 121-125.
• [6] A. Boussayoud, A. Abderrezzak, On Some Identities and Generating Functions for Hadamard Product, Electron. J. Math. Analysis Appl.5(2), (2017), 89-97.
• [7] A. Boussayoud, M. Bolyer, M. Kerada, On Some Identities and Symmetric Functions for lucas and pell numbers, Electron. J. Math. Analysis Appl. 5(1), (2017), 202-207, .
• [8] A. Boussayoud, Symmetric functions for k-Pell Numbers at negative indices, Tamap Journal of Mathematics and Statistics. 1ID20, (2017), 1-8.
• [9] A. Boussayoud, On some identities and generating functions for Pell-Lucas numbers, Online.J. Anal. Comb. 12 1-10, (2017).
• [10] A. Boussayoud, N. Harrouche, Complete Symmetric Functions and k- Fibonacci Numbers, Commun. Appl. Anal. 20, (2016), 457-467.
• [11] C. Bolat, H Kose, On the Properties of k-Fibonacci Numbers, Int. J. Contemp. Math. Sciences. 5, 1097-1105, (2010).
• [12] P. Catarino, On Some Identities and Generating Functions for k- Pell Numbers, Int. Journal of Math. Analysis. 7, 1877-1884, (2013).
• [13] M. Asci, E. Gurel, Gaussian Jacobsthal and Gaussian Jacobsthal Lucas polynomials, Notes Number Theory Discrete Math.19, 25-36, (2013).
• [14] D. Jhala, G.P.S. Rathore, K Sisodiya, Some Properties of k-Jacobsthal Numbers with Arithmetic Indexes, Turkish Journal of Analysis and Number.2(4), (2014), 119-124.
• [15] A.F Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Q. 3, 161–176, (1965).
• [16] S. Falcon, A. Plaza, On the Fibonacci k- numbers, Chaos, Salutions & Fractals. 32, (2007), 1615-1624.
• [17] S. Falcon, A. Plaza, The k- Fibonacci sequence and the Pascal 2-triangle, Chaos, Salutions & Fractals. 33, (2008), 38-49.
• [18] N. Y. Ozgur, J. Sokol, On starlike functions connected with k-Fibonacci numbers, Bull. Malays. Math. Sci. Soc. 38 (2015), 249-258.
• [19] N. Y. Ozgur, S. U car, New presentations for real numbers, Math. Sci.Appl. E-Notes 3 (2015), 13–17.
• [20] N. Y. Ozgur, S. U car, O. Oztun c, Complex factorizations of the k-Fibonacci and k-Lucas numbers, An. S tiint. Univ. Al. I. Cuza Ia si. Mat., 62 (2016), 13–20.