Generalized Voigt functions and their derivatives

Abstract

This paper deals with a special class of functions called generalized Voigt functions H(n)(x,a) and G(n)(x,a) and their partial derivatives, which are useful in the theory of polarized spectral line formation in stochastic media. For n=0 they reduce to the usual Voigt and Faraday–Voigt functions H(x,a) and G(x,a). A detailed study is made of these new functions. Simple recurrence relations are established and employed for the calculation of the functions themselves and of their partial derivatives. Asymptotic expansions are given for large values of x and a. They are used to examine the range of applicability of the recurrence relations and to construct a numerical algorithm for the calculation of the generalized Voigt functions and of their derivatives valid in a large (x,a) domain. It is also shown that the partial derivatives of the usual H(x,a) and G(x,a) can be expressed in terms of H(n)(x,a) and G(n)(x,a).