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

- Closed-form analytical approximations of Voigt function in terms of rational functions, inverse tangents and logarithms.
- Reasonable for large y, but substantial accuracy problems for small y.
- Moderate computational efficiency.

Rational approximations for the Gauss function can be used to construct closed-form 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 that supposedly “good” approximations of the integrand do not necessarily provide good approximations of the integral, i.e. Voigt function.