Geodesic
An inequality for the coefficients of a cosine polynomial
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 427-428.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We prove: If $$ \frac 12+\sum_{k=1}^{n}a_k(n)\cos (kx)\geq 0 \text{ for all } x\in [0,2\pi ), $$ then $$ 1-a_k(n)\geq \frac 12 \frac{k^2}{n^2} \text{ for } k=1,\dots ,n. $$ The constant $1/2$ is the best possible.
Classification : 26D05, 42A05
Keywords: cosine polynomials; inequalities 
@article{CMUC_1995__36_3_a2,
     author = {Alzer, Horst},
     title = {An inequality for the coefficients of a cosine polynomial},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {427--428},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1995},
     mrnumber = {1364482},
     zbl = {0833.26012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a2/}
}
TY  - JOUR
AU  - Alzer, Horst
TI  - An inequality for the coefficients of a cosine polynomial
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1995
SP  - 427
EP  - 428
VL  - 36
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a2/
LA  - en
ID  - CMUC_1995__36_3_a2
ER  - 
%0 Journal Article
%A Alzer, Horst
%T An inequality for the coefficients of a cosine polynomial
%J Commentationes Mathematicae Universitatis Carolinae
%D 1995
%P 427-428
%V 36
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a2/
%G en
%F CMUC_1995__36_3_a2
Alzer, Horst. An inequality for the coefficients of a cosine polynomial. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 427-428. http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a2/