[Tex/LaTex] Erf function in LaTeX

Question

Is there a way to easily compute the erf function (or the cumulative distribution function of the normal law) in LaTeX?

Currently, I use pgf to make computation, but I did not find a way to compute erf using pgf.

I would be happy to use any package that is available to compute erf, or any custom solution to compute that function.

Answer 1

For precise values, I recommend externalizing the calculation, here gnuplot is used.

Code (needs --shell-escape enabled)

\documentclass{article}
\usepackage{amsmath,pgfmath,pgffor}
\makeatletter
\def\qrr@split@result#1 #2\@qrr@split@result{\edef\erfInput{#1}\edef\erfResult{#2}}
\newcommand*{\gnuplotErf}[2][\jobname.eval]{%
    \immediate\write18{gnuplot -e "set print '#1'; print #2, erf(#2);"}%
    \everyeof{\noexpand}
    \edef\qrr@temp{\@@input #1 }%
    \expandafter\qrr@split@result\qrr@temp\@qrr@split@result
}
\makeatother
\DeclareMathOperator{\erf}{erf}
\begin{document}
\foreach \x in {-50,...,50}{%
\pgfmathparse{\x/50}%
\gnuplotErf{\x/50.}%
$ x = \pgfmathresult = \erfInput, \erf(x) = \erfResult$\par
}
\end{document}

Output