An inequality for the coefficients of a cosine polynomial

Alzer, Horst. "An inequality for the coefficients of a cosine polynomial." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 427-428. <http://eudml.org/doc/247706>.

@article{Alzer1995,
abstract = {We prove: If \[ \frac\{1\}\{2\}+\sum \_\{k=1\}^\{n\}a\_k(n)\cos (kx)\ge 0 \text\{ for all \} x\in [0,2\pi ), \] then \[ 1-a\_k(n)\ge \frac\{1\}\{2\} \frac\{k^2\}\{n^2\} \text\{ for \} k=1,\dots ,n. \] The constant $1/2$ is the best possible.},
author = {Alzer, Horst},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {cosine polynomials; inequalities; inequality; coefficients; cosine polynomial},
language = {eng},
number = {3},
pages = {427-428},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An inequality for the coefficients of a cosine polynomial},
url = {http://eudml.org/doc/247706},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Alzer, Horst
TI - An inequality for the coefficients of a cosine polynomial
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 427
EP - 428
AB - We prove: If \[ \frac{1}{2}+\sum _{k=1}^{n}a_k(n)\cos (kx)\ge 0 \text{ for all } x\in [0,2\pi ), \] then \[ 1-a_k(n)\ge \frac{1}{2} \frac{k^2}{n^2} \text{ for } k=1,\dots ,n. \] The constant $1/2$ is the best possible.
LA - eng
KW - cosine polynomials; inequalities; inequality; coefficients; cosine polynomial
UR - http://eudml.org/doc/247706
ER -