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.