Voigt Transform and Umbral Image

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

An adaptive Gaussian quadrature for the Voigt function

We evaluate an adaptive Gaussian quadrature integration scheme suitable for the numerical evaluation of generalized redistribution in frequency functions. The latter are indispensable ingredients for “full non-LTE” radiation transfer computations, assuming potential deviations of the velocity distribution of massive particles from the usual Maxwell–Boltzmann distribution. A first validation is made with computations of the usual Voigt profile.