Abstract The trapezoidal formula is known to achieve exponential convergence when calculating infinite integrals of bilateral rapidly decreasing functions. Even when considering unilateral rapidly decreasing functions, the trapezoidal formula can be made to converge exponentially by applying an appropriate conformal map to the integrand, as proposed by Stenger. This study modifies the conformal map to achieve a better convergence rate. Furthermore, aiming for verified numerical integration, we specify a rigorous error bound for the modified quadrature formula. Numerical examples comparing the modified to the existing formula are considered.

中文翻译：

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单边快速递减函数无穷积分的修正Stenger求积公式及其理论误差界

摘要 在计算双边快速递减函数的无穷大积分时，已知梯形公式可以实现指数收敛。即使在考虑单边快速递减函数时，也可以通过将适当的共形映射应用于被积函数来使梯形公式以指数方式收敛，如 Stenger 所提出的。本研究修改了共形图以实现更好的收敛速度。此外，为了验证数值积分，我们为修改后的求积公式指定了严格的误差界限。考虑将修改后的公式与现有公式进行比较的数值示例。