Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate Erf efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix Erf function using MatrixFunction:

Simple exact values are generated automatically:

Values at infinity:

Find the zero of Erf:

Plot the Erf function:

Plot the real part of :

Plot the imaginary part of :

Erf is defined for all real and complex values:

Erf takes all real values between –1 and 1:

Erf is an odd function:

Erf has the mirror property :

Erf is an analytic function of x:

It has no singularities or discontinuities:

Erf is nondecreasing:

Erf is injective:

Erf is not surjective:

Erf is neither non-negative nor non-positive:

Erf is neither convex nor concave:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of Erf:

Definite integral of an odd integrand over an interval centered at the origin is 0:

More integrals:

Taylor expansion for Erf:

Plot the first three approximations for Erf around :

General term in the series expansion of Erf:

Asymptotic expansion of Erf:

Erf can be applied to a power series:

Compute the Fourier transform of Erf using FourierTransform:

LaplaceTransform:

Integral definition of the error function:

Argument involving basic arithmetic operations:

The two-argument form gives the difference:

Error function in terms of the incomplete Gamma:

Represent in terms of MeijerG using MeijerGReduce:

Erf can be represented as a DifferentialRoot:

TraditionalForm formatting: