Results 151 to 160 of about 18,585 (194)

Inequalities for Alternating Trigonometric Sums

Results in Mathematics, 2012
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Alzer, Horst, Liu, Xiuping, Shi, Xiquan
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Sharp inequalities for trigonometric sums

Mathematical Proceedings of the Cambridge Philosophical Society, 2003
Summary: We prove the following two theorems: (I) Let \(n\geq 1\) be a (fixed) integer. Then we have for \(\theta\in(0,\pi)\): \[ \sum^n_{k=1}{\cos(k\theta)\over k}\leq-\log\left(\sin\left({\theta\over 2}\right)\right)+{\pi-\theta\over 2}+\sigma_n, \] with the best possible constant \(\sigma_n=\sum^n_{k=1}(-1)^k/k\).
Alzer, H., Koumandos, S., Alzer, H., Koumandos, S.   +3 more
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A Sharp Inequality for a Trigonometric Sum

Mediterranean Journal of Mathematics, 2012
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Alzer, H., Koumandos, S., Alzer, H., Koumandos, S.   +3 more
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On a trigonometric inequality of Askey and Steinig

Asymptotic Analysis, 2018
In 1974, Askey and Steinig showed that for [Formula: see text] and [Formula: see text], [Formula: see text] We prove that [Formula: see text] and that the alternating sums [Formula: see text] satisfy [Formula: see text] Both inequalities hold for all [Formula: see text] and [Formula: see text].
Horst Alzer, Man Kam Kwong
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On Two Trigonometric Inequalities of Carslaw and Gasper

Results in Mathematics, 2022
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Horst Alzer, Man Kam Kwong
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A trigonometrical inequality

Mathematical Proceedings of the Cambridge Philosophical Society, 1951
AbstractThe inequality iswhich is established by an elementary argument and is shown to lead directly to the evaluation of the integraland to the expression of sin x as an infinite product.
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Turan's Inequalities for Trigonometric Polynomials

Journal of the London Mathematical Society, 1996
We present a technique for establishing inequalities of the form \[ c |f |_\infty \leq \int^{2 \pi}_0 \varphi \biggl (\bigl |f^{(k)} (t) \bigr |\biggr) dt \leq M |f |_\infty \] in the set of all trigonometric polynomials of order \(n\) which have only real zeros. The function \(\varphi\) is assumed to be convex and increasing on \([0, \infty)\).
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A further note on trigonometrical inequalities

Mathematical Proceedings of the Cambridge Philosophical Society, 1950
1. The aim of this note is to prove theTheorem. Letwhere the λnare real andand letThenA similar result holds for infinite seriesconverging uniformly in [−T, T].
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An Approach to Trigonometric Inequalities

Mathematics Magazine, 1970
(1970). An Approach to Trigonometric Inequalities. Mathematics Magazine: Vol. 43, No. 5, pp. 254-257.
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Inequalities for trigonometric polynomials

Approximation Theory and its Applications, 1997
Summary: Let \(t_n(x)\) be any real trigonometric polynomial of degree \(n\) such that \(\| t_n\|_\infty\leq 1\). Here, we are concerned with obtaining the best possible upper estimate of \[ \int^{2\pi}_0 | t^{(k)}_n(x)|^q dx\Biggl/\int^{2\pi}_0| t^{(k)}_n(x)|^{q- 2}dx, \] where \(q>2\).
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