  The double exponential formula, or the DE formula, is a high-precision
integration formula using a change of variables called a DE transformation;
whereas there is a disadvantage that it is sensitive to singularities of an
integrand near the real axis. To overcome this disadvantage, Slevinsky and
Olver (SIAM J. Sci. Comput., 2015) attempted to improve it by constructing
conformal maps based on the locations of singularities. Based on their ideas,
we construct a new transformation formula. Our method employs special types of
the Schwarz-Christoffel transformations for which we can derive their explicit
form. Then, the new transformation formula can be regarded as a generalization
of the DE transformations. We confirm its effectiveness by numerical
experiments.
