Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3473
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
First Page
1932
Last Page
1943
Recommended Citation
MUFID, MUHAMMAD SYIFA'UL and SZALAY, LASZLO
(2023)
"Interpolation polynomials associated to linear recurrences,"
Turkish Journal of Mathematics: Vol. 47:
No.
7, Article 7.
https://doi.org/10.55730/1300-0098.3473
Available at:
https://journals.tubitak.gov.tr/math/vol47/iss7/7
