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

 See Also

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