A faster procedure for the calculation of the J(ξ, β) function

One of the biggest difficulties in obtaining an analytical expression for the J(ξ, β) function is its explicit dependence on the Doppler broadening function ψ(x,ξ). The objective of this paper is to present a method for the fast and accurate calculation for the J(ξ, β) function based on the recent advances in the calculation of the Doppler broadening function and on a systematic analysis of its integrand. The methodology proposed uses an analytical formulation for the calculation of ψ(x, ξ) and a representation in series for error functions with complex argument. The results were satisfactory from the accuracy and processing time standpoint and are an option to other calculation methods found in the literature.