A New Generalization of Fibonacci Polynomials

Abstract

The Fibonacci sequences, which have an increasing place in scientific studies and are the most wellknown among the number sequences, first appeared in Leonardo Fibonacci's book 'Liber Abaci', which contains many basic problems, in a rabbit problem. Fibonacci sequences were obtained by writing down the monthly total number of new rabbits born by mating only once per month, initially one female and one male rabbit. This sequence, which is obtained by adding the two numbers before it; It continues as 1,1,2,3,5,8,13,21,34,55,89,144,23, 377, . . . In this paper, we define a new generalization of Fibonacci Polynomials. The relationship between known Fibonacci Polynomials and ???? −Fibonacci Polynomials are given. Some properties of these polynomials have been obtained. Also, matrix presentations of the new family of polynomials are found. Finally, we give Cassini's identity for the polynomials.