Question

what is an Error function?

Answer 1

... the one that symbolize by erf(x)...

Answer 2

This function is defined for all complex arguments x.

For floating-point arguments the error functions erf, erfc, and erfi return floating-point values. The implemented exact values are:

erf(0) = 0, erf(∞) = 1, erf(- ∞) = - 1, erf(i ∞) = i ∞, erf(- i ∞) = - i ∞,

For all other arguments, the error function returns symbolic function calls.

For the function erf with floating-point arguments of large absolute value, internal numerical underflow or overflow can happen.

The error functions erf(x) = 1 - erfc(x) and erfi(x) = i (erfc(x i) - 1) return corresponding values for large arguments. See Example 2.

MuPAD® can simplify expressions that contain error functions and their inverses. For real values x, the system applies the following simplification rules:

inverf(erf(x)) = inverf(1 - erfc(x)) = inverfc(1 - erf(x)) = inverfc(erfc(x)) = x,

inverf(- erf(x)) = inverf(erfc(x) - 1) = inverfc(1 + erf(x)) = inverfc(2 - erfc(x)) = - x

For any value x, the system applies the following simplification rules:

inverf(- x) = - inverf(x),

inverfc(2 - x) = - inverfc(x),

erf(inverf(x)) = erfc(inverfc(x)) = x.

erf(inverfc(x)) = erfc(inverf(x)) = 1 - x.

Answer 3

... thanks for this information... this function is widely used in the field of Communication Engineering and wondering some of the approximations made for some value of x....