On the very accurate evaluation of the Voigt functions

摘要

Here we indicate how a particular version of the trapezoidal integration with residue correction for the evaluation of the Voigt functions indicated by us previously can be easily extended to serve the purpose of reference value generation. Specifically by resorting to quadruple precision, we demonstrate a reliable computation with a minimum of 30 digit accuracy for the Voigt functions H(x, a) and G(x, a). Compared to the prescription of Boyer et al., this method reduces the computational cost several fold when very high reference accuracy is the aim. In addition we show that when both the parameters x and a are less than unity, the series of Faddeeva et al. can be profitably used for the required evaluation instead of this quad rature. (C) 2018 Elsevier Ltd. All rights reserved.