EFFICIENT METHOD FOR EVALUATION OF THE COMPLEX PROBABILITY FUNCTION - VOIGT FUNCTION AND ITS DERIVATIVES

An efficient method is developed to evaluate the function w(z)=e-z(1+(2i/√π)∫z 0et dt) for the complex argument z = x + iy. The real part of w(z) is the Voigt function describing spectral line profiles; the imaginary part can be used to compute derivatives of the spectral line shapes, which are useful, e.g. in least-squares fitting procedures. As an example of the method a simple and fast FORTRAN subroutine is listed in the Appendix from which w(z) in the entire y ≥ 0 half-plane can be calculated, the maximum relative error being less than 2 × 10-6 and 5 × 10-6 for the real and imaginary parts, respectively. © 1979.