Numerical integration of Fourier integrals by the optimal quadrature formula exact for hyperbolic functions.

This paper studies the problem of construction of the optimal quadrature formula for numerical calculation of Fourier integrals. Applying the discrete analogue of the differential operator d 4 d x 4 − 2 d 2 d x 2 + 1 and using its properties we obtain the optimal quadrature formula wich is exact for hyperbolic functions sinh(x) and cosh(x), we get explicit expressions for the coefficients of the optimal quadrature formula. The obtained optimal quadrature formulas can be used in problems where Fourier transformations are used. [ABSTRACT FROM AUTHOR]