On the k -Lucas Numbers and Lucas Polynomials

Ali Boussayoud^1, , Mohamed Kerada¹ and Nesrine Harrouche²

¹LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria

²Department of Mathematics, University of Jordan, Amman 11942, Jordan

Cite this paper:
Ali Boussayoud, Mohamed Kerada and Nesrine Harrouche. On the k -Lucas Numbers and Lucas Polynomials. Turkish Journal of Analysis and Number Theory. 2017; 5(4):121-125. doi: 10.12691/tjant-5-4-1

Abstract

In this paper, we introduce an operator in order to derive some new symmetric properties of -Lucas numbers and Lucas polynomials. By making use of the operator defined in this paper, we give some new generating functions for -Lucas numbers and Lucas polynomials.

Keywords:
k-Lucas numbers Lucas polynomials generating functions

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References:

[1]	A. Abderrezzak, Généralisation de la transformation d'Euler d'une série formelle, Adv. Math. 103, 1994, 180-195.
[2]	A. Abderrezzak, M. Kerada, A. Boussayoud, Generalization of Some Hadamard Product, Commun. Appl. Anal. 20(3), 301-306, (2016).
[3]	A. Boussayoud, M. Boulyer, M. Kerada, On Some Identities and Symmetric Functions for Lucas and Pell Numbers, Electron .J.Math. AnalysisAppl. 5, 2017, 202-207.
[4]	A. Boussayoud, N. Harrouche, Complete Symmetric Functions and k - Fibonacci Numbers, Commun. Appl. Anal. 20(4), 2016, 457-467.
[5]	A. Boussayoud, M. Kerada, M. Boulyer, A simple and accurate method for determination of some generalized sequence of numbers, Int. J. Pure Appl. Math.108, 2016, 503-511.
[6]	A. Boussayoud, A. Abderrezzak, M. Kerada, Some applications of symmetric functions, Integers. 15, A#48, 2015, 1-7.
[7]	A. Boussayoud, M. Kerada, A. Abderrezzak, A Generalization of Some Orthogonal Polynomials, Springer Proc. Math. Stat. 41, 2013, 229-235.
[8]	M. Merca, A Generalization of the symmetry between complete and elementary symmetric functions, Indian J. Pure Appl. Math. 45, 2014, 75-89.
[9]	S. Falcon, A. Plaza, On the Fibonacci k - numbers, Chaos, Sulutions & Fractals. 32, 2007, 1615-1624.
[10]	S. Falcon, On the k -Lucas Numbers of Arithmetic Indexes, Appl. Math. 3, 2012, 1202-1206.
[11]	S. Falcon, On the k-Lucas numbers, J.Math.Comput.Sci. 2, 2012, 425-434.
[12]	S. Falcon, On the complex k-Fibonacci numbers, Cogent Math. 3, 2016, 1-9.
[13]	T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, 2001.
[14]	Y. K.Gupta, V. H. Badshah, M. Singh, K. Sisodiya, Some Identities of Tribonacci Polynomials, Turkish Journal of Analysis and Number Theory. 4, 2016, 20-22.
[15]	Y. K.Gupta, V. H. Badshah, M. Singh, K. Sisodiya, Diagonal Function of k-Lucas Polynomials, Turkish Journal of Analysis and Number Theory. 3, 2015, 49-52.