Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3473
Keywords
Linear recurrence, interpolation polynomial, finite difference
First Page
1932
Last Page
1943
Recommended Citation
MUFID, M. S, & SZALAY, L (2023). Interpolation polynomials associated to linear recurrences. Turkish Journal of Mathematics 47 (7): 1932-1943. https://doi.org/10.55730/1300-0098.3473
