A modified Stenger’s quadrature formula for infinite integrals of unilateral rapidly decreasing functions and its theoretical error bound

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.