# What is the error function used for?

## What is the error function used for?

The error function erf is a special function. It is widely used in statistical computations for instance, where it is also known as the standard normal cumulative probability.

## What is inverse error function?

The inverse error function inverf x occurs in the solution of nonlinear heat and diffusion problems [ 1 ]. It provides exact solutions when the diffu- sion coefficient is concentration dependent, and may be used to solve certain moving interface problems. erfc y = 1 – erf y.

What is the correct definition of an error function?

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: This integral is a special (non-elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations.

### What is error function in digital communication?

Error function The complementary error function represents the area under the two tails of zero mean Gaussian probability density function of variance. . The error function gives the probability that the parameter lies outside that range.

### How do you use the error function in Excel?

You can use the IFERROR function to trap and handle errors in a formula. IFERROR returns a value you specify if a formula evaluates to an error; otherwise, it returns the result of the formula….Examples.

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Formula Description Result

What is the inverse of erfc?

The inverse complementary error function erfcinv(x) is defined as erfcinv ( erfc ( x ) ) = x .

#### What is erf in calculator?

The error function (often abbreviated to erf, also known as the Gaussian error function) is a special function that we encounter in applied mathematics and mathematical physics, e.g., in solutions to the heat equation.

#### Is erf odd or even?

The error function is defined for all values of x and is considered an odd function in x since erf x = −erf (−x).

How do you solve an integral error?

Integration by Parts:

1. Let u=erf(x) and dv=dt.
2. du=2√πe−x2 and v=x.
3. By the integration by parts formula ∫udv=uv−∫vdu.
4. ∫erf(x)dx=xerf(x)−∫2√πxe−x2dx.
5. To evaluate the remaining integral, let u=−x2.
6. Then du=−2xdx and so.
7. −∫2√πxe−x2dx=1√π∫eudu.
8. ∫erf(x)dx=xerf(x)+e−x2√π+C.