Theoretical comparison of two conformal maps combined with the trapezoidal formula for the semi-infinite integral of exponentially decaying functions

Abstract

It is well-known that the trapezoidal formula is an accurate quadrature formula for the infinite integral of exponentially decaying functions. Even for the semi-infinite integral of exponentially decaying functions, the trapezoidal formula works accurately combined with a conformal map proposed by Lund. Another conformal map for this case was introduced by Muhammad and Mori, and their map worked better in all the numerical comparisons conducted so far. Therefore, the conformal map by Muhammad and Mori is expected to give better results in all instances than that by Lund. This paper proves the conjecture.