The Error Function (ERF) calculator helps you determine the value of this special function for any given real number 'x'. Essential in probability theory, statistics, and partial differential equations, the ERF is closely related to the cumulative distribution function of the normal distribution.
Formula:
The Error Function (ERF), often denoted as erf(x), is a special mathematical function that arises in probability, statistics, and partial differential equations. It is defined as:
erf(x) = (2/√π) ∫0x e-t² dt
Where:
x: The real number at which to evaluate the error function.e: Euler's number, approximately 2.71828.π: Pi, approximately 3.14159.∫0x: Represents the definite integral from 0 to x.e-t²: The integrand, a Gaussian function.
The error function describes the shape of the Gaussian integral, particularly useful for calculating probabilities within a normal distribution.