This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Erfc

 Erfc[z]gives the complementary error function .
• 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.
Evaluate numerically:
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:
Simple exact values are generated automatically:
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:
Use FunctionExpand to convert to other functions:
Compose with inverse functions:
Integrals:
Integral transforms:
Solve a transcendental equation:
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:
A neat continued fraction:
Its limit can be expressed through Erfc:
New in 2