Inequalities for two sine polynomials
Horst Alzer ; Stamatis Koumandos
Colloquium Mathematicae, Tome 106 (2006), p. 127-134 / Harvested from The Polish Digital Mathematics Library
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We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0,π) we have α≤∑j=1n-11/(n²-j²)sin(jx)≤β, with the best possible constant bounds α = (15-√2073)/10240 √(1998-10√2073) = -0.1171..., β = 1/3. (II) The inequality 0<∑j=1n-1(n²-j²)sin(jx) holds for all even integers n ≥ 2 and x ∈ (0,π), and also for all odd integers n ≥ 3 and x ∈ (0,π - π/n].

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:284357 
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     title = {Inequalities for two sine polynomials},
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     year = {2006},
     pages = {127-134},
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Horst Alzer; Stamatis Koumandos. Inequalities for two sine polynomials. Colloquium Mathematicae, Tome 106 (2006) pp. 127-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm105-1-11/