scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
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

Book
01 Jun 1965

226 citations

Journal ArticleDOI
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

Journal ArticleDOI
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


Network Information
Related Topics (5)
Operator theory
18.2K papers, 441.4K citations
81% related
Banach space
29.6K papers, 480.1K citations
79% related
Differential algebraic equation
13.2K papers, 421.6K citations
79% related
Sobolev space
19.8K papers, 426.2K citations
79% related
Numerical partial differential equations
20.1K papers, 703.7K citations
79% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20233
202216
20191
20181
201732
201635