errorFn — Special

View versions (2)

Interface

#include <codecogs/maths/special/errorfn.h>

using namespace Maths::Special;

double errorFn( double x )

The Error Function is defined by equation

$$erf(x) \equiv \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt$$

(1)

and has the shape \graph x=-4:4

References

Eric W. Weisstein. "Erf." From MathWorld--A Wolfram Web Resource
http://mathworld.wolfram.com/Erf.html
Stephen L. Moshier, Cephes Mathematical Library (the rational

approximations used here for |x|>=1, split at |x|=8, are Moshier's).

Example 1

#include <codecogs/maths/special/errorfn.h>
#include <stdio.h>
using namespace Maths::Special;
int main(  )
{
  double x = 0.5;
  printf("\n errorFn(%f) = %f", x, errorFn(x));
  return getchar();
}

Output:

errorFn(0.500000) = 0.520500

Parameters

the upper limit of the integral

Returns

the value of the Error Function evaluated at the given abscissa, accurate to full double precision for any finite x (for |x| beyond about 6 the true value is indistinguishable from $\pm 1$ at double precision, and this returns exactly that)

Interactive Calculator

Result –