A continuous Euler transformation and its application to the Fourier transform of a slowly decaying function

The Euler transformation is a linear sequence transformation to accelerate the convergence of an alternating series. The sequence of weights of the transformation is extended to a continuous weight function which can accelerate Fourier-type integrals including Hankel transforms with a slowly convergent integrand. We show that the continuous weight function can also be used to compute the Fourier transform of a slowly decaying function using FFT.