While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case of unilateral rapidly decreasing functions. To address this issue, Stenger proposed the application of a conformal map to the integrand such that it transforms into bilateral rapidly decreasing functions. Okayama and Hanada modified the conformal map and provided a rigorous error bound for the modified formula. This paper proposes a further improved conformal map, with two rigorous error bounds provided for the improved formula. Numerical examples comparing the proposed and existing formulas are also given.

尽管将梯形公式应用于双边快速递减函数的无穷积分时可以实现指数收敛，但在单边快速递减函数的情况下却无法做到这一点。为了解决这个问题，Stenger提出将共形图应用于被积物，以便将其转换为双边快速递减的函数。冈山和花田修改了共形图，并为修改后的公式提供了严格的误差范围。本文提出了进一步改进的共形图，为改进的公式提供了两个严格的误差范围。还给出了比较建议的公式和现有公式的数值示例。