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Declaration: Erf (x: double): double;

The function Erf returns the error function (which is a special case of the incomplete gamma function). The error function is defined as follows:

Typical application of the error function: when the results of a series of measurements are described by a normal distribution with a standard deviation sigma and an expected value of zero, then

erf (a*sqrt(2)/2/sigma))

returns the probability that the error of a single measurement lies between -a and +a.

Hint 1: The complementary error function (often denoted as erfc) can be easily calculated from Erf: erfc(x) = 1-Erf(x).

Hint 2: A faster routine to calculate the error function is ErfApprox.