error function

The error functionDlmfDlmfPlanetmath erf: is defined as follows:


The complementary error functionDlmfDlmf erfc: is defined as


The name “error function” comes from the role that these functionsMathworldPlanetmath play in the theory of the normal random variable. It is also worth noting that the error function is a special case of the confluent hypergeometric functions and of the Mittag-Leffler functionDlmfMathworldPlanetmath.

Note.  By Cauchy integral theorem (, the choice path of integration in the definition of erf is irrelevant since the integrand is an entire functionMathworldPlanetmath. In the definition of erfc, the path may be taken to be a half-line parallel to the positive real axis with endpoint z.

Title error function
Canonical name ErrorFunction
Date of creation 2013-03-22 14:46:51
Last modified on 2013-03-22 14:46:51
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 10
Author rspuzio (6075)
Entry type Definition
Classification msc 33B20
Related topic AreaUnderGaussianCurve
Related topic ListOfImproperIntegrals
Related topic UsingConvolutionToFindLaplaceTransform
Defines complementary error function