Topic
Proofs of trigonometric identities
About: Proofs of trigonometric identities is a research topic. Over the lifetime, 865 publications have been published within this topic receiving 8412 citations.
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TL;DR: In this paper, it was shown that the standard notion of a trigonometric polynomial does not agree with a more naive, but reasonable notion of trigonometri...
Abstract: As an application of Bezout's theorem from algebraic geometry, we show that the standard notion of a trigonometric polynomial does not agree with a more naive, but reasonable notion of trigonometri...
295 citations
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189 citations
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TL;DR: In this paper, it was shown that for any trigonometric polynomial of order the following inequality holds for all natural numbers, and this inequality may be considered a generalization of the inequalities of S. N. Bernstein and A. Zygmund.
Abstract: Let be the set of nondecreasing functions defined on which admit a representation , where the function is convex (below) on . To the class belong, for example, the functions , , when , and also any function which is convex on . In this paper it is shown, in particular, that if , then for any trigonometric polynomial of order the following inequality holds for all natural numbers : This inequality may be considered a generalization of the inequalities of S. N. Bernstein and A. Zygmund. Bibliography: 16 titles.
142 citations
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TL;DR: Using the linear stage representation of a Runge-Kutta method given in Albrecht's approach, the methods which integrate trigonometric polynomials exactly are derived.
141 citations