An inequality for the coefficients of a cosine polynomial
Alzer, Horst
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 427-428 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1995-01-01
Classification:  26D05,  42A05 
@article{118770,
     author = {Horst Alzer},
     title = {An inequality for the coefficients of a cosine polynomial},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {427-428},
     zbl = {0833.26012},
     mrnumber = {1364482},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118770}
}

Alzer, Horst. An inequality for the coefficients of a cosine polynomial. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 427-428. http://gdmltest.u-ga.fr/item/118770/

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