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The Error function and related functions are defined in Abramowitz and Stegun, Handbook of Mathematical Functions, Chapter 7
The Error Function erf(z) (A&S 7.1.1)
See also flag erfflag
.
The Complementary Error Function erfc(z) (A&S 7.1.2)
erfc(z) = 1-erf(z)
The Imaginary Error Function.
erfi(z) = -%i*erf(%i*z)
Generalized Error function Erf(z1,z2)
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
.
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
.
Default value: false
When T erfc, erfi, erf_generalized, fresnel_s and fresnel_c are transformed to erf.
Default value: false
Enables transformation to a Hypergeometric representation for fresnel_s and fresnel_c
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