Interpolation polynomials associated to linear recurrences

Authors: MUHAMMAD SYIFA'UL MUFID, LASZLO SZALAY

Abstract: Assume that $(G_n)_{n\in\mathbb{Z}}$ 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 $(t,G_t)$ ($n_0\le t\le n_1$). 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.

Keywords: Linear recurrence, interpolation polynomial, finite difference

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