Optimized computation of the voigt and complex probability functions

Methods for computing the complex probability function w(z) = e^?z2 erfc (?iz), which is related to the Voigt spectrum line profiles, are developed. The basic method is a rational approximation, minimizing the relative error of the imaginary part on the real axis. It is complemented by other methods in order to increase efficiency and to overcome the inevitable failure of any rational approximation near the real axis. The procedures enable one to evaluate both real and imaginary parts of w(z) with high relative accuracy. The methods are simple, as demonstrated by a sample FORTRAN program.