eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2017-06-07 5 4 121 125 10.12691/tjant-5-4-1 TJANT2017541 article Ali Boussayoud aboussayoud@yahoo.fr 1 Mohamed Kerada 1 Nesrine Harrouche 2 LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria Department of Mathematics, University of Jordan, Amman 11942, Jordan 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. http://pubs.sciepub.com/tjant/5/4/1/tjant-5-4-1.pdf k-Lucas numbers Lucas polynomials generating functions