### 15.6 Error Function

The Error function and related functions 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`.

  ·Special functions

Function: erfc (z)

  The Complementary Error Function erfc(z) (A&S 7.1.2)

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

  ·Special functions

Function: erfi (z)

  The Imaginary Error Function.

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

  ·Special functions

Function: erf_generalized (z1,z2)

  Generalized Error function Erf(z1,z2)

  ·Special functions

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`.

  ·Special functions

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`.

  ·Special functions

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