Abstract
The double exponential formula is well-known as a powerful numerical quadrature rule, but is weak to integral transforms of a certain kind (for example, Fourier transform, Hankel transform, Bessel transform and Hilbert transform). When the double exponential formula is applied to these transforms, the number of function evaluations increases very much. In this paper, we propose a powerful and efficient computation method for these transforms. The idea of the new method is based on the double exponential transformation and the sinc approximation.
