Some unified presentations of the Voigt functions

The principal object of this note is to provide a natural further step toward the unified presentations of the Voigh functionsK(x, y) andL(x, y) which play a rather important role in such diverse fields of physics as astrophysical spectroscopy and the theory of neutron reactions. Explicit representations for these functions, given in terms of some relatively more familiar special functions of one and two variables, are potentially useful in finding many other needed (numerical or analytical) properties of the Voigt functions. Several erroneous recent contributions to the theory of Voigt functions, including (for example) the main result of A. Siddiqui (1990), are also corrected here.