Double exponential formulas for numerical integration

Abstract

A family of numerical quadrature formulas is introduced by application of the trapezoidal rule to infinite integrals which result from the given integrals ∫baf(x)dx by suitable variable transformations x = ∅(u). These formulas are characterized by having double exponential asymptotic behavior of the integrands in the resulting infinite integrals as u-→±∞, and it is shown both analytically and numerically that such formulas are generally optimal with respect to the ecomony of the number of sampling points. © 1974, Research Institute forMathematical Sciences. All rights reserved.