Abstract
A simple and efficient method is proposed for the calculation of the complex error function, including its real part, which is the Voigt spectrum line profile. This procedure is based on the observation by Harstad that a rational approximation to the error function, which is the value of the complex error function on the imaginary axis, analytically continues off this axis upon replacement of y by y- ix. The error involved in this approximation can be minimized by choice of an optimal set of coefficients according to methods developed by Curtis and Osborne. An analysis shows that the results are sufficiently accurate for most applications over the whole complex plane, but with the error increasing toward the real axis. The procedure is simpler and faster than previous methods, requiring only two arithmetic statements for coding in FORTRAN. Comparisons are presented of the time required for various methods on various IBM computer systems which supports this conclusion.
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