The **`erf` function** is defined in the `<math.h>` header file in C. It takes in a single parameter: a `double` value. It then computes the error function of the given argument and returns a value of type `double`. 

The #key# error function: also known as Gauss error function  #key# in mathematics is defined as follows:

> erf $z$ = $\frac{2}{\sqrt{\pi}}$ $\int_{0}^{arg} e^{-t^2} dt$ 

> The argument to the `erf` function serves as the upper limit in the integral above.

The error function is most often used in probability and statistics. It integrates the normal distribution and gives the probability that a normally distributed random variable Y (with mean 0 and variance ½) falls into the range [−x, x].

The illustration below shows how `erf` function works: 

# Declaration

The `erf` function is defined as follows:

```C
double erf(double arg);
```
It takes in a single value of type `double` and computes its error function. It then returns the answer of type `double`.

# Example
The following code snippet shows how we can use the `erf` function:


#include <stdio.h> // Including header file for printf function
#include <math.h>  // Including header file for erf function

int main (){

  double param, result;
  param = 2.0;
  result = erf(param);
  printf("erf (%f) = %f\n", param, result);
  return 0;
}

# Error handling

The `erf` function returns special values for certain arguments:

* If the argument is +-0, +-0 is returned
* If the argument is +-$\infty$, +- $\infty$ is returned
* If the argument is `NAN`, `NAN` is returned

# Example

The following code snippet shows how error handling in the `erf` function works:

#include <stdio.h> // Including header file for printf function
#include <math.h>  // Including header file for erf function

int main (){

  printf("erf (%f) = %f\n", 0.0, erf(0.0));
  return 0;
}

What is erf in C?

Defined in <math.h>, the erf function computes the error function of a double value, commonly used in probability and statistics.