Fast and accurate expression for the Voigt function. Application to the determination of uranium M linewidths

The Voigt function is the convolution between a Gaussian and a Lorentzian distribution. The numerical implementation of this function is required in diverse areas of physics and applied mathematics. An explicit representation for the Voigt function is developed in terms of series of trigonometric and hyperbolic functions. The obtained expression permits a very fast evaluation of Voigt profiles with a degree of accuracy higher than the one required for spectroscopy applications. In addition, this expression is implemented in a numerical algorithm of parameter optimization in electron probe microanalysis, and applied to determine natural linewidths for several transitions to the uranium M levels.