An assessment of some closed-form expressions for the Voigt function II: Utilizing rational approximations for the Gauss function

Franz Schreier
2017 Journal of Quantitative Spectroscopy and Radiative Transfer  
Rational approximations for the Gauss function can be used to construct closedform expressions of the Voigt function K(x, y) in terms of rational functions, logarithms and inverse trigonometric functions. The comparison with accurate reference values indicates a relative accuracy in the percent range for y 1, but serious problems for smaller y. Furthermore, these expressions are not competitive with other algorithms with respect to computational speed. Both accuracy and speed tests indicate
more » ... supposedly "good" approximations of the integrand do not necessarily provide good approximations of the integral, i.e. Voigt function.
doi:10.1016/j.jqsrt.2017.05.035 fatcat:563jfkc2w5h63p5npgw7mpcrhu