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 a Lorentzian function), the function N(a, b) defined as the convolution of Gaussian and dispersion distributions as well as the complex error function erf(a + ib), all in terms of the Kummer functions M(α, γ, a2). The expansions are valid for all values of the parameter a (the relation between Lorentzian and Gaussian widths at the half maxima). Previous analytical works were known only when the parameter a ≤ 1, or were based on numerical interpolations or empirical approximations. Also, new series and asymptotic expansions are presented.