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.
 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
 Szegö C.: Orthogonal polynomials
. American Mathematical Society, New York, 1959. MR 0106295