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Keywords:
numerical analysis
numerical analysis
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.
References:
[1] Hammer P. C., Wicke H. H.: Quadrature formulas involving derivatives of the integrand. Mathematics of Computation 69, 3-7 (1960). DOI 10.1090/S0025-5718-1960-0110191-0 | MR 0110191 | Zbl 0121.11701
[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
[3] Szegö C.: Orthogonal polynomials. American Mathematical Society, New York, 1959. MR 0106295
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