A new series for approximating Voigt functions

Abstract

A Voigt function is the convolution of a Gaussian and a Cauchy, or Lorentzian, density. The computation of these functions is required in problems arising in a variety of subjects such as nuclear reactors, atmospheric transmittance, and spectroscopy. This letter presents a new series for the approximate computation of Voigt functions. The derivation is accomplished using straightforward Fourier techniques, and it yields computable error bounds between the approximation and the Voigt function. The approach also permits a simple derivation of an asymptotic expansion for large argument values.