The Voigt Profile as a Sum of a Gaussian and a Lorentzian Functions, when the Weight Coefficient Depends Only on the Widths Ratio

Assuming that V(x) approximate to (1 - mu) G(1) (x) + mu L-1(x) is a very good approximation of the Voigt function, in this work we analytically find mu from mathematical properties of V(x). G(1)(x) and L-1(x) represent a Gaussian and a Lorentzian function, respectively, with the same height and HWHM as V(x), the Voigt function, x being the distance from the function center. mu is obtained as a function of a, a being the ratio of the Lorentz width to the Gaussian width. We find that, the Voigt function calculated with the expression we have obtained for mu, deviates from the exact value less than 0.5% with respect to the peak value.