Erf
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- Erf[z] is the integral of the Gaussian distribution, given by
.
- Erf[z0,z1] is given by
.
- Erf[z] is an entire function of z with no branch cut discontinuities.
- For certain special arguments, Erf automatically evaluates to exact values.
- Erf can be evaluated to arbitrary numerical precision.
- Erf automatically threads over lists.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (33)
Numerical Evaluation (5)
Specific Values (3)
Visualization (2)
Function Properties (4)
Integration (3)
Indefinite integral of Erf:
Definite integral of an odd integrand over an interval centered at the origin is 0:
Series Expansions (4)
Integral Transforms (2)
Function Identities and Simplifications (3)
Function Representations (4)
Error function in terms of the incomplete Gamma:
Represent in terms of MeijerG using MeijerGReduce:
Erf can be represented as a DifferentialRoot:
TraditionalForm formatting:
Applications (2)
Express the CDF of NormalDistribution in terms of the error function:
The cumulative probabilities for values of the normal random variable lie between -n σ and n σ:
The solution of the heat equation for a piecewise‐constant initial condition:
Properties & Relations (3)
Compose with inverse functions:
Solve a transcendental equation:

Erf appears in special cases of many mathematical functions:
Possible Issues (3)
Neat Examples (1)
Its limit can be expressed through Erf:
Text
Wolfram Research (1988), Erf, Wolfram Language function, https://reference.wolfram.com/language/ref/Erf.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "Erf." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Erf.html.
APA
Wolfram Language. (1988). Erf. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Erf.html