Numerical quadrature of Fourier transform integrals. II

were presented. In this note we present odd-point Gaussian formulae. In addition. by making use of the fact that in both the even and odd point schemes the points are equally spaced, we derive a method for evaluating the integrals in Eq. (1) for a large number of values of the parameter x from a knowledge of the functions +(k) or At(k) at a specified set of points {ki}. In other words, we remove, to some extent, one of the disadvantages of the method described in [1], to wit, that for each different value of x the functions ^t and 4 had to be evaluated at an entirely new set {ki}. This disadvantage is also inherent in a scheme proposed by Goldberg and Varga [2], whose method also appears to be somewhat more difficult to apply than that used here.