On some properties of Chebyshev polynomials

Hacène Belbachir, and Farid Bencherif. "On some properties of Chebyshev polynomials." Discussiones Mathematicae - General Algebra and Applications 28.1 (2008): 121-133. <http://eudml.org/doc/276945>.

@article{HacèneBelbachir2008,
abstract = {Letting $T_\{n\}$ (resp. $U_\{n\}$) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences $(X^\{k\}T_\{n-k\})_\{k\}$ and $(X^\{k\}U_\{n-k\})_\{k\}$ for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space $_\{n\}[X]$ formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also $T_\{n\}$ and $U_\{n\}$ admit remarkableness integer coordinates on each of the two basis.},
author = {Hacène Belbachir, Farid Bencherif},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Chebyshev polynomials; integer coordinates},
language = {eng},
number = {1},
pages = {121-133},
title = {On some properties of Chebyshev polynomials},
url = {http://eudml.org/doc/276945},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Hacène Belbachir
AU - Farid Bencherif
TI - On some properties of Chebyshev polynomials
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 1
SP - 121
EP - 133
AB - Letting $T_{n}$ (resp. $U_{n}$) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences $(X^{k}T_{n-k})_{k}$ and $(X^{k}U_{n-k})_{k}$ for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space $_{n}[X]$ formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also $T_{n}$ and $U_{n}$ admit remarkableness integer coordinates on each of the two basis.
LA - eng
KW - Chebyshev polynomials; integer coordinates
UR - http://eudml.org/doc/276945
ER -