抄録
In this paper we derive a formula for indefinite integration of analytic functions over (-1,s) where -1 < s < 1, with possible singularity at the end points s = ±1 of the integrand, by means of the sinc approximation followed by the double exponential transformation. It can be regarded as a double exponential analogue of the formula by S. Haber. The error of our formula behaves approximately as exp (-c_1N/log c_2N) where N is the number of function evaluations of the integrand. This error term shows a much faster convergence when N becomes large than that of the formula by Haber. Several numerical examples also indicate high efficiency of our formula.
