MATLAB Function Reference Volume 1: A - E - Bad Request

2erf, erfc, erfcx, erfinv, erfcinv
Purpose Error functions
erf, erfc, erfcx, erfinv, erfcinv
Syntax Y = erf(X) Error function
Y = erfc(X) Complementary error function
Y = erfcx(X) Scaled complementary error function
X = erfinv(Y) Inverse error function
X = erfcinv(Y) Inverse complementary error function
Definition The error function erf(X) is twice the integral of the Gaussian distribution
with 0 mean and variance of 1 ⁄ 2 .
erf( x)
2
------ e
π
t2
x
= –
∫ dt
0
The complementary error function erfc(X) is defined as
erfc( x)
2
------ e
π
t2
∞
= –
∫ dt
= 1 – erf( x)
x
The scaled complementary error function erfcx(X) is defined as
erfcx( x)
e
For large X, erfcx(X) is approximately
x2 = erfc( x)
⎛ 1
------ ⎞1
--
⎝ π ⎠x
Description Y = erf(X) returns the value of the error function for each element of real
array X.
Y = erfc(X) computes the value of the complementary error function.
Y = erfcx(X) computes the value of the scaled complementary error function.
X = erfinv(Y) returns the value of the inverse error function for each element
of Y. Elements of Y must be in the interval [-1 1]. The function erfinv
satisfies y = erf( x)
for – 1 ≤ y ≤1and – ∞ ≤ x ≤ ∞ .
X = erfcinv(Y) returns the value of the inverse of the complementary error
function for each element of Y. Elements of Y must be in the interval [0 2].
The function erfcinv satisfies y = erfc( x)
for 2 ≥ y ≥ 0 and – ∞ ≤ x ≤∞.
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