Erf(x) Error Function

By definition,

Erf(x) = 2/SqRt(Pi) * Integral{0, x}[Exp(-t^2)] dt.

If |x| >= 10^−8,

Erf(x) = 1 − ErfC(x),
else
Erf(x) = 2*x/SqRt(Pi) * Sum[(−x^2)^j / (j!*(2*j + 1))], j >= 0.

This sum is needed for small x to minimize the relative error in Erf(x).

See: Erf -- From MathWorld
And: Wolfram Function Evaluation -- Erf

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Changes last made on Monday, 06-Aug-07 20:47:15 PDT