Constrained near-minimax rational approximations to Dawson's integral

Abstract

This paper develops a family of rational functions for computing Dawson's integral F( x). The near-minimax rational approximation formulas we derive have positive coefficients and provide a simple, uniform method for calculating F( x). Unlike some frequently used methods, our approach does not involve segmented approximation to cover the whole approximation interval | x| < ∞. The rational approximation formulas we present are particularly useful in applications where modest accuracy is sufficient and computational efficiency and convenience are paramount.