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:

    “Children, then, acquire social skills not so much from adults as from their interactions with one another. They are likely to discover through trial and error which strategies work and which do not, and later to reflect consciously on what they have learned.”
    —Zick Rubin (20th century)

    “The fact remains that the human being in early childhood learns to consider one or the other aspect of bodily function as evil, shameful, or unsafe. There is not a culture which does not use a combination of these devils to develop, by way of counterpoint, its own style of faith, pride, certainty, and initiative.”
    —Erik H. Erikson (1904–1994)