An alternative analytical formulation for the Voigt function applied to resonant effects in nuclear processes

The Voigt function H( a, v) is defined as the convolution of the Gaussian and Lorentzian functions. Recent papers puplished in different areas of physics emphasize the importance of the fast and accurate calculation of the Voigt function for different orders of magnitude of variables a and v. An alternative analytical formulation for the Voigt function is proposed in this paper. This formulation is based on the solution of the non-homogeneous ordinary differential equation, satisfied by the Voigt function, using the Frobenius and parameter variation methods. The functional form of the Voigt function, as proposed, proved simple and precise. Systematic tests are accomplished demonstrating some advantages with other existent methods in the literature and with the numeric method of reference.