Evaluation of the Asymmetric Voigt Profile and Complex Error Functions in Terms of the Kummer Functions

Abstract

In this work we present the explicit representations of the Voigt function K(a,b) (the convolution between a Gaussian and Lorentzian function), the function N(a,b) as the convolution of Gassian and dispersion distributions as well as the complex error function erf(a+ib), all in terms of the the Kummer functions M(α,ς,α2). The expansion are valid for all values of the parameter α (the relations between Lorentzian and Gaussian widths at the half maxima). Previos analytical works were know only when the parameter α ≤ 1, or were based on numerical interpolations or emperical aproximations. Also, new series and asymtotic expansion are presented.