A sharp bound for a sine polynomial
Horst Alzer ; Stamatis Koumandos
Colloquium Mathematicae, Tome 96 (2003), p. 83-91 / Harvested from The Polish Digital Mathematics Library
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We prove that |∑k=1nsin((2k-1)x)/k|<Si(π)=1.8519... for all integers n ≥ 1 and real numbers x. The upper bound Si(π) is best possible. This result refines inequalities due to Fejér (1910) and Lenz (1951).

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:285080 
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Horst Alzer; Stamatis Koumandos. A sharp bound for a sine polynomial. Colloquium Mathematicae, Tome 96 (2003) pp. 83-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-8/