Interpolation polynomials associated to linear recurrences

Abstract

: Assume that ( G n ) n ∈ Z is an arbitrary real linear recurrence of order k . In this paper, we examine the classical question of polynomial interpolation, where the basic points are given by ( t, G t ) ( n 0 ≤ t ≤ n 1 ). The main result is an explicit formula depends on the explicit formula of G n and on the finite difference sequence of a specific sequence. It makes it possible to study the interpolation polynomials essentially by the zeros of the characteristic polynomial of ( G n ) . During the investigations, we developed certain formulae related to the finite differences