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On a positive sine sum

100%

Koumandos S.

Colloquium Mathematicum

1996

tom 71

nr 2

243-251

Inequalities for two sine polynomials

63%

Alzer H., Koumandos S.

Colloquium Mathematicum

2006

tom 105

nr 1

127-134

We prove: (I) For all integers n ≥ 2 and real numbers x ∈ (0,π) we have $α ≤ ∑_{j=1}^{n-1} 1/(n²-j²) sin(jx) ≤ β$, with the best possible constant bounds α = (15-√2073)/10240 √(1998-10√2073) = -0.1171..., β = 1/3. (II) The inequality $0 < ∑_{j=1}^{n-1} (n²-j²)sin(jx)$ 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].

A sharp bound for a sine polynomial

63%

Alzer H., Koumandos S.

Colloquium Mathematicum

2003

tom 96

nr 1

83-91

We prove that $|∑_{k=1}^{n} sin((2k-1)x)/k| < Si(π) = 1.8519...$ 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).

Ograniczanie wyników

3 Colloquium Mathematicum

3 Koumandos S.

2 Alzer H.

1 2006

1 2003

1 1996

Wyniki wyszukiwania

On a positive sine sum

Inequalities for two sine polynomials

A sharp bound for a sine polynomial