An efficient method for evaluation of the complex probability function: The Voigt function and its derivatives

An efficient method is developed to evaluate the function w(z)=e^-z2(1+(2i/√π)∫^z₀e^t2dt) 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.