Of the 3 routines here that can be used to evaluate the "Z function", the Plasma Dispersion Function Z(zeta), I'm guessing that the best one is wofz.f (or Zfun.f90, which uses subroutine wofz). At least it is based on the most recently published algorithm. I downloaded wofz.f from http://www.netlib.org/toms/680. It is based on the 1990 paper:

G.P.M. Poppe, C.M.J. Wijers, "More Efficient Computation of the Complex Error-Function", ACM Trans. Math. Software 16, 47 (1990).

```The plasma dispersion function Z(z) is related to the w(z) function
calculated by wofz.f by the simple relationship:

Z(z) = i*sqrt(Pi) * w(z)

w(z) is sometimes called the Voight function or Faddeeva's function, and is
related to the complementary error function by:

w(z) = exp(-z**2)erfc(-iz)

w(z) = exp(-z**2)(1 - erf(-iz))

The plasma dispersion function  Pdf(z) = Z(z) is usually defined as

Z(z) = 1/SQRT(Pi) * Integral(-Inf,+Inf) exp(-t**2)/(t-z) dt ,

(this form is valid only for z in the upper half complex plane...)

```

The Poppe and Wijers 1990 paper discusses various way in which this algorithm has been made significantly faster than previous algorithms. These algorithms tend to be based on various asymptotic series or continued fraction approximations (chosen to be optimal in various regions of parameter space). I wonder if it might be possible to develop an even faster algorithm based on rational function approximations that are fit to the exact result. It would require refitting if a different level of accuracy is desired, but might give some speed advantages.

--Greg Hammett, Oct. 27, 2006