erf - Maple Help

MTM

 erf
 the error function
 erfc
 the complementary error function

 Calling Sequence erf(x) erfc(x)

Parameters

 x - array or algebraic expression

Description

 • The error function is defined as

$\mathrm{erf}\left(x\right)=\frac{2\left({{\int }}_{0}^{x}{ⅇ}^{-{t}^{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}t\right)}{\sqrt{\mathrm{\pi }}}$

 • erf(x) will evaluate by default only when the result is an exact value, or when the input x is a floating-point number.  When x is a symbolic expression, it will remain in function form so that it can be manipulated symbolically  or as part of a larger expression.
 • If x is an array, the result is an elementwise mapping over x.
 • erfc(x) is the complementary error function, that is, $1-\mathrm{erf}\left(x\right)$.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $\mathrm{erf}\left(⟨⟨1.286495,2.540680⟩|⟨7.354414,6.899301⟩⟩\right)$
 $\left[\begin{array}{cc}{0.9311463225}& {1.}\\ {0.9996731879}& {1.}\end{array}\right]$ (1)
 > $\mathrm{erfc}\left(⟨⟨1.286495,2.540680⟩|⟨7.354414,6.899301⟩⟩\right)$
 $\left[\begin{array}{cc}{0.06885367755}& {2.460874117}{×}{{10}}^{{-25}}\\ {0.0003268121343}& {1.720286965}{×}{{10}}^{{-22}}\end{array}\right]$ (2)

Compatibility

 • The MTM[erfc] command was introduced in Maple 2021.
 • For more information on Maple 2021 changes, see Updates in Maple 2021.