Calculation of the Voigt Function in the Region of Very Small Values of the Parameter a Where the Calculation Is Notoriously Difficult

The Voigt function is the convolution of a Lorentzian and a Guaussian density. The computation of these functions is required in several problems arising in a variety of physicochemical subjects; such as nuclear reactors, atmospheric transmittance and spectroscopy. In this work we suggest using a new formula for the calculation of the Voigt function. Our formula is a new integral representation for the Voigt function that gives the perfect results for the Voigt function calculation and is easily calculable. We give also a comparison between our results of calculation of Voigt function for the very small values of the parameter a, where the calculation is notoriously difficult, with those of the various algorithms of other authors.