## org.apache.commons.math3.special Class Erf

```java.lang.Object org.apache.commons.math3.special.Erf
```

`public class Erfextends Object`

This is a utility class that provides computation methods related to the error functions.

Version:
\$Id: Erf.java 1416643 2012-12-03 19:37:14Z tn \$

Method Summary
`static double` `erf(double x)`
Returns the error function.
`static double` ```erf(double x1, double x2)```
Returns the difference between erf(x1) and erf(x2).
`static double` `erfc(double x)`
Returns the complementary error function.

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Method Detail

### erf

`public static double erf(double x)`
Returns the error function.

erf(x) = 2/√π 0x e-t2dt

This implementation computes erf(x) using the `regularized gamma function`, following Erf, equation (3)

The value returned is always between -1 and 1 (inclusive). If `abs(x) > 40`, then `erf(x)` is indistinguishable from either 1 or -1 as a double, so the appropriate extreme value is returned.

Parameters:
`x` - the value.
Returns:
the error function erf(x)
Throws:
`MaxCountExceededException` - if the algorithm fails to converge.
See Also:
`Gamma.regularizedGammaP(double, double, double, int)`

### erfc

`public static double erfc(double x)`
Returns the complementary error function.

erfc(x) = 2/√π x e-t2dt
= 1 - `erf(x)`

This implementation computes erfc(x) using the `regularized gamma function`, following Erf, equation (3).

The value returned is always between 0 and 2 (inclusive). If `abs(x) > 40`, then `erf(x)` is indistinguishable from either 0 or 2 as a double, so the appropriate extreme value is returned.

Parameters:
`x` - the value
Returns:
the complementary error function erfc(x)
Throws:
`MaxCountExceededException` - if the algorithm fails to converge.
Since:
2.2
See Also:
`Gamma.regularizedGammaQ(double, double, double, int)`

### erf

```public static double erf(double x1,
double x2)```
Returns the difference between erf(x1) and erf(x2). The implementation uses either erf(double) or erfc(double) depending on which provides the most precise result.

Parameters:
`x1` - the first value
`x2` - the second value
Returns:
erf(x2) - erf(x1)

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