Definition:Error Function

Definition

The error function is the following improper integral, considered as a real function $\erf : \R \to \R$:

$\map {\erf} x = \ds \dfrac 2 {\sqrt \pi} \int_0^x \map \exp {-t^2} \rd t$

where $\exp$ is the real exponential function.

Also see

• Definition:Complementary Error Function
• Definition:Gaussian Integral

• Results about the error function can be found here.

Sources

• 1965: Murray R. Spiegel: Theory and Problems of Laplace Transforms ... (previous) ... (next): Chapter $1$: The Laplace Transform: Some Special Functions: $\text {III}$. The Error function
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): error function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): error function