Topic
Integration using Euler's formula
About: Integration using Euler's formula is a research topic. Over the lifetime, 527 publications have been published within this topic receiving 6451 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1930
TL;DR: In this article, the authors present a quadrature algorithm for the integral form where ψ(x) is a function with a limited number of turning points in the range of integration and k is a constant which may take up large values.
Abstract: 1. Integrals of the form where ψ(x) is a function with a limited number of turning-points in the range of integration and k is a constant which may take up large values, frequently occur in investigations in mathematical physics, and their computation by quadratures is often desirable.
643 citations
423 citations
1 Jan 1988
220 citations
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.
177 citations
TL;DR: In this article, it was shown that certain trigonometric B -splines satisfy a recurrence relation similar to the one for polynomial splines, and a trigonometric version of Marsden's identity is given.
137 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 6 |
| 2024 | 2 |
| 2023 | 18 |
| 2022 | 26 |
| 2019 | 1 |
| 2018 | 3 |