Error Function Calculator
The error function (erf), also known as the Gauss error function, is a special function that occurs in probability, statistics, and partial differential equations.
\( \text{erf}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt \)
It represents the probability that a random variable with a normal distribution of mean 0 and variance 1/2 will fall in the range [-x, x].
\( \text{erfc}(x) = 1 - \text{erf}(x) = \frac{2}{\sqrt{\pi}} \int_x^\infty e^{-t^2} dt \)
It is closely related to the Q-function, which is the tail probability of the standard normal distribution.
\( \text{erf}^{-1}(y) \) finds the value `x` such that `erf(x) = y`.
It is defined for inputs `y` in the interval `(-1, 1)`.
\( \text{erfc}^{-1}(y) = \text{erf}^{-1}(1-y) \)
It is defined for inputs `y` in the interval `(0, 2)`.
Calculate erf(x), erfc(x), and their inverses, and visualize the functions.