On a positive sine sum
Inequalities for two sine polynomials
We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0,π) we have , with the best possible constant bounds α = (15-√2073)/10240 √(1998-10√2073) = -0.1171..., β = 1/3. (II) The inequality 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].
A sharp bound for a sine polynomial
We prove that 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).
A note on a monotonicity property of Bessel functions.
Positive trigonometric sums and applications.
On a class of integrals involving a Bessel function times Gegenbauer polynomials.
Some inequalities for the sine integral.
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