Inequalities for two sine polynomials
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We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0, π) we have (Formula Presented) with the best possible constant bounds (Formula Presented) (II) The inequality (Formula Presented) 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]. © 2006, Instytut Matematyczny. All rights reserved.