BUILT-IN MATHEMATICA SYMBOL

Erfc

Erfc[z]
gives the complementary error function

.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

Erfc[z] is given by .

For certain special arguments, Erfc automatically evaluates to exact values.

Erfc can be evaluated to arbitrary numerical precision.

Erfc automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Evaluate numerically:

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Scope (6)

Evaluate for complex arguments:

Evaluate to high precision:

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

Erfc threads element-wise over lists:

Simple exact values are generated automatically:

TraditionalForm formatting:

Generalizations & Extensions (2)

Erfc can be applied to a power series:

Infinite arguments give symbolic results:

Applications (3)

CDF of normal distribution:

Probability that a random value is greater than n

:

Solution of the heat equation for piecewise-constant initial condition:

A check that the solution fulfills the heat equation:

Plot of the solution for different times:

Defined the scaled complementary error function via HermiteH function:

Properties & Relations (5)

Use FunctionExpand to convert to other functions:

Compose with inverse functions:

Integrals:

Integral transforms:

Solve a transcendental equation:

Possible Issues (3)

For large arguments, intermediate values may underflow:

The error function for large negative real-part arguments can be very close to 2:

Very large arguments can give unevaluated results:

Neat Examples (1)

A neat continued fraction:

Its limit can be expressed through Erfc: