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

The complementary error function in mathematics is defined as follows:

> erfc $z$ = $1- \frac{2}{\sqrt{\pi}}$ $\int_{0}^{arg} e^{-t^2} dt$ 

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

> The argument to the `erfc` function serves as the lower 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 complementary error function, combined with its series expansion, provides approximate expressions for small and large values of x.

The figure below shows the plot of the `erfc` function:

The illustration below shows how `erfc` function works:

# Declaration

The `erfc` function is defined as follows:

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

# Error handling

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

|  Special Value | Returned   |
| - | - |
| +INFINITY | +0  |
| -INFINITY | +2  |
| `NAN`| `NAN`|

# Examples

The following code snippet shows how we can use the `erfc` function:


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

int main (){

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

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

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

int main (){

  printf("erfc (%f) = %f\n", INFINITY, erfc(INFINITY));
  printf("erfc (%f) = %f\n", -INFINITY, erfc(-INFINITY));
  return 0;
}

What is erfc in C?

erfc computes the complementary error function of a given double value, used in probability and statistics. It returns special values for certain arguments.