erf - Maple Help

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convert/erf

convert to Error Function

convert/erfc

convert to Complementary Error Function

 Calling Sequence convert( expr, erf ); convert( expr, erfc );

Parameters

 expr - any expression

Description

 • convert/erf converts expressions involving the complementary error function, the iterated integrals of the complementary error function and/or Dawson's integral to the equivalent form using the error function.
 • convert/erfc converts expressions involving the error function to the equivalent form using the complementary error function.

Examples

 > $\mathrm{convert}\left(\mathrm{erfc}\left(x\right),\mathrm{erf}\right)$
 ${1}{-}{\mathrm{erf}}{}\left({x}\right)$ (1)
 > $\mathrm{convert}\left(\mathrm{erfc}\left(2,x\right),\mathrm{erf}\right)$
 $\frac{{{x}}^{{2}}}{{2}}{-}\frac{{{x}}^{{2}}{}{\mathrm{erf}}{}\left({x}\right)}{{2}}{-}\frac{{x}}{{2}{}\sqrt{{\mathrm{\pi }}}{}{{ⅇ}}^{{{x}}^{{2}}}}{+}\frac{{1}}{{4}}{-}\frac{{\mathrm{erf}}{}\left({x}\right)}{{4}}$ (2)
 > $\mathrm{convert}\left(,\mathrm{erfc}\right)$
 $\frac{{{x}}^{{2}}}{{2}}{-}\frac{{{x}}^{{2}}{}\left({1}{-}{\mathrm{erfc}}{}\left({x}\right)\right)}{{2}}{-}\frac{{x}}{{2}{}\sqrt{{\mathrm{\pi }}}{}{{ⅇ}}^{{{x}}^{{2}}}}{+}\frac{{\mathrm{erfc}}{}\left({x}\right)}{{4}}$ (3)
 > $\mathrm{convert}\left(\mathrm{dawson}\left(x\right),\mathrm{erf}\right)$
 $\frac{{-}\frac{{I}}{{2}}{}\sqrt{{\mathrm{\pi }}}{}{\mathrm{erf}}{}\left({I}{}{x}\right)}{{{ⅇ}}^{{{x}}^{{2}}}}$ (4)

 See Also