erf
The Error Function
erfc
The Complementary Error Function and its Iterated Integrals
erfi
The Imaginary Error Function
Calling Sequence
Parameters
Description
Examples
References
erf(x)
erfc(x)
erfc(n, x)
erfi(x)
x
-
algebraic expression
n
algebraic expression, understood to be an integer ≤ −1
The error function is defined for all complex x by
erf⁡x=2⁢∫0xⅇ−t2ⅆtπ
The complementary error function is defined by
erfc⁡x=1−erf⁡x=1−2π12⁢∫0xⅇ−t2⁢ⅆt
The iterated integrals of the complementary error function are defined by
erfc⁡−1,x=2π⁢ⅇ−x2
erfc⁡n,x=∫x∞erfc⁡n−1,t⁢ⅆt⁢⁢⁢n≥0
(Note erfc⁡0,x=erfc⁡x.)
The imaginary error function is defined by
erfi⁡x=−I⁢erf⁡I⁢x=2π⁢∫0xⅇt2⁢ⅆt
All of these functions are entire.
erf(infinity);
1
erf(3);
erf⁡3
evalf((2));
0.9999779095
erfc(3.);
0.00002209049700
erf(1.-1.*I);
1.316151282−0.1904534692⁢I
erfc(1.5-2.85*I);
−62.82064889−10.56167495⁢I
diff(erf(x),x);
2⁢ⅇ−x2π
diff(erfc(5,x), x);
−erfc⁡4,x
erfi(-x);
−erfi⁡x
series(erfi(x),x,4);
2π⁢x+23⁢1π⁢x3+O⁡x5
expand(erfc(2,x),x);
x22−x2⁢erf⁡x2−x⁢ⅇ−x22⁢π+14−erf⁡x4
convert((11),erfc);
x22−x2⁢1−erfc⁡x2−x⁢ⅇ−x22⁢π+erfc⁡x4
Erdelyi, A. Higher Transcendental Functions. McGraw-Hill, 1953. Vol. 2.
See Also
convert
dawson
Fresnel
initialfunctions
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