  In this paper, we propose a numerical method of computing an integral whose
integrand is a slowly decaying oscillatory function. In the proposed method, we
consider a complex analytic function in the upper-half complex plane, which is
defined by an integral of the Fourier-Laplace transform type, and we obtain the
desired integral by the analytic continuation of this analytic function onto
the real axis using a continued fraction. We also remark that the proposed
method is related to hyperfunction theory, a theory of generalized functions
based on complex function theory. Numerical examples show the effectiveness of
the proposed method.
