# Article

 Title: Numerical integration with highly oscillating weight functions (English) Author: Mikloško, Jozef Language: English Journal: Aplikace matematiky ISSN: 0373-6725 Volume: 15 Issue: 2 Year: 1970 Pages: 133-145 Summary lang: English Summary lang: Slovak . Category: math . Summary: The paper describes a new numerical method for the computation of integrals with the weight function exp$(ikx)$, $k$ integer, which can be used for improper and multiple integrals. The compound rules of this method use parameters, of weighted quadratures of Gauss type which are tabulated for various $k$. The using of the method especially for high $k$ is demonstrated by numerical experiments. (English) Keyword: numerical analysis MSC: 65-55 idZBL: Zbl 0191.16304 idMR: MR0256566 DOI: 10.21136/AM.1970.103277 . Date available: 2008-05-20T17:47:31Z Last updated: 2020-07-28 Stable URL: http://hdl.handle.net/10338.dmlcz/103277 . Reference: [1] Hammer P. C., Wicke H. H.: Quadrature formulas involving derivatives of the integrand.Mathematics of Computation 69, 3-7 (1960). Zbl 0121.11701, MR 0110191, 10.1090/S0025-5718-1960-0110191-0 Reference: [2] Mikloško J.: Numerical integration with weight functions cos kx, sin kx on the $[0,2 \pi/t]$, t = 1, 2, ....Aplikace matematiky, 3, 1969, 179-194. MR 0246510 Reference: [3] Szegö C.: Orthogonal polynomials.American Mathematical Society, New York, 1959. MR 0106295 .

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