the approximation is still of order , i.e. . This approximation has a relative accuracy of over the full wavelength range of , provided that . In addition to its high accuracy, the function is easy to implement as well as computationally fast. It is widely used in the field of quasar absorption line analysis. Pseudo-Voigt approximation The pseudo-Voigt profile (or pseudo-Voigt function) is an approximation of the Voigt profile V(x) using a linear combination of a Gaussian curve G(x) and a Lorentzian curve L(x) instead of their convolution. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes. The mathematical definition of the normalized pseudo-Voigt profile is given by with . is a function of full width at half maximum (FWHM) parameter. There are several possible choices for the parameter. A simple formula, accurate to 1%, is where now, is a function of Lorentz (), Gaussian () and total () Full width at half maximum (FWHM) parameters. The total FWHM () parameter is described by: The width of the Voigt profile The full width at half maximum (FWHM) of the Voigt profile can be found from the widths of the associated Gaussian and Lorentzian widths. The FWHM of the Gaussian profile is The FWHM of the Lorentzian profile is An approximate relation (accurate to within about 1.2%) between the widths of the Voigt, Gaussian, and Lorentzian profiles is: By construction, this expression is exact for a pure Gaussian or Lorentzian. A better approximation with an accuracy of 0.02% is given by (originally found by Kielkopf) Again, this expression is exact for a pure Gaussian or Lorentzian. In the same publication, a slightly more precise (within 0.012%), yet significantly more complicated expression can be found. References External links http://jugit.fz-juelich.de/mlz/libcerf, numeric C library for complex error functions, provides a function voigt(x, sigma, gamma) with approximately 13–14 digits precision. The original article is : Voigt, Woldemar, 1912, ''Das Gesetz der Intensitätsverteilung innerhalb der Linien eines Gasspektrums'', Sitzungsbericht der Bayerischen Akademie der Wissenschaften, 25, 603 (see also: http://publikationen.badw.de/de/003395768) Continuous distributions Spectroscopy Special functions Probability distributions with non-finite variance