Error Function

In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape which occurs in probability, statistics and partial differential equations. It is defined as:

The complementary error function, denoted erfc, is defined as

\begin{align} \operatorname{erfc}(x) & = 1-\operatorname{erf}(x) \\ & = \frac{2}{\sqrt{\pi}} \int_x^{\infty} e^{-t^2}\,dt. \end{align}

The imaginary error function, denoted erfi, is defined as

When the error function is evaluated for arbitrary complex arguments z, the resulting complex error function is usually discussed in scaled form as the Faddeeva function:

Read more about Error Function:  The Name "error Function", Properties, Approximation With Elementary Functions, Applications, Related Functions, Implementations, Table of Values

Famous quotes containing the words error and/or function:

    “Mistakes are made on two counts: an argument is either based on error or incorrectly developed.”
    —Thomas Aquinas (c. 1225–1274)

    “As a medium of exchange,... worrying regulates intimacy, and it is often an appropriate response to ordinary demands that begin to feel excessive. But from a modernized Freudian view, worrying—as a reflex response to demand—never puts the self or the objects of its interest into question, and that is precisely its function in psychic life. It domesticates self-doubt.”
    —Adam Phillips, British child psychoanalyst. “Worrying and Its Discontents,” in On Kissing, Tickling, and Being Bored, p. 58, Harvard University Press (1993)