(maxima.info)Error Function

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15.6 Error Function
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The Error function and related funtions are defined in Abramowitz and
Stegun, Handbook of Mathematical Functions, Chapter 7

 -- Function: erf (<z>)

     The Error Function erf(z) (A&S 7.1.1)

     See also flag 'erfflag'.

 -- Function: erfc (<z>)
     The Complementary Error Function erfc(z) (A&S 7.1.2)

     'erfc(z) = 1-erf(z)'

 -- Function: erfi (<z>)
     The Imaginary Error Function.

     'erfi(z) = -%i*erf(%i*z)'

 -- Function: erf_generalized (<z1>,<z2>)
     Generalized Error function Erf(z1,z2)

 -- Function: fresnel_c (<z>)
     The Fresnel Integral C(z) = integrate(cos((%pi/2)*t^2),t,0,z).
     (A&S 7.3.1)

     The simplification fresnel_c(-x) = -fresnel_c(x) is applied when
     flag 'trigsign' is true.

     The simplification fresnel_c(%i*x) = %i*fresnel_c(x) is applied
     when flag '%iargs' is true.

     See flags 'erf_representation' and 'hypergeometric_representation'.

 -- Function: fresnel_s (<z>)
     The Fresnel Integral S(z) = integrate(sin((%pi/2)*t^2),t,0,z).
     (A&S 7.3.2)

     The simplification fresnel_s(-x) = -fresnel_s(x) is applied when
     flag 'trigsign' is true.

     The simplification fresnel_s(%i*x) = -%i*fresnel_s(x) is applied
     when flag '%iargs' is true.

     See flags 'erf_representation' and 'hypergeometric_representation'.

 -- Option variable: erf_representation
     Default value: false

     When T erfc, erfi, erf_generalized, fresnel_s and fresnel_c are
     transformed to erf.

 -- Option variable: hypergeometric_representation
     Default value: false

     Enables transformation to a Hypergeometric representation for
     fresnel_s and fresnel_c