Shifted rectangular quadrature rule approximations to Dawsonʹs integral F(x)

This paper investigates the relationship between some rapidly convergent series of exponential functions for computing Dawsonʹs integral. These series are the result of approximating a certain improper integral by a shifted rectangular quadrature rule. Dawsonʹs original method and a more recent expansion due to Rybicki are shown to be special cases of our quadrature approach. An error bound is derived to compare the accuracy of the resulting approximations.