SOME EXTENSIONS OF PROPERTIES OF THE SEQUENCE OF RECIPROCAL FIBONACCI POLYNOMIALS

This paper is, in a sense, dual to the Fibonacci Association paper by J. R. Howell [4]. On the other hand, interest in the reciprocal Fibonacci-like polynomials is caused by the very effective propositions 7 and 4 of [3]. It is also the intention of this paper to draw the attention of the Fibonacci Association audience to the vast area of applications of its activities in the domain of computational techniques allowing one to perform quantitative comparisons among various data organizations in the framework defined by the authors of [3]. Let Wn(x) be a polynomial in the variable x; xe(c,rf)cR and dQg(Wn(x)) = N. We define the reciprocal polynomial ofWn(x) as follows. Definition 1: Wn(x) = x N Wn(- \ (1) The purpose of this paper is to describe the reciprocal polynomials of Fibonacci-like polynomials that are defined by the recursion formula [4] where a and h are real constants. g„+2(x) = axg„+l(x) + hg„(x), (2) It is easy to verify that the reciprocal Fibonacci-like polynomials satisfy Indeed, if degg^x) = m, then