Gaussian function | Special hypergeometric functions | Functions related to probability distributions | Analytic functions

Error function

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: This integral is a special (non-elementary) sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real. In statistics, for non-negative values of x, the error function has the following interpretation: for a random variable Y that is normally distributed with mean 0 and standard deviation 1/√2, erf x is the probability that Y falls in the range [−x, x]. Two closely related functions are the complementary error function (erfc) defined as and the imaginary error function (erfi) defined as where i is the imaginary unit (Wikipedia).

Error function
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(New Version Available) Inverse Functions

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Define an inverse function. Determine if a function as an inverse function. Determine inverse functions.

From playlist Determining Inverse Functions

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Abramowitz and Stegun | Domain coloring | Confluent hypergeometric function | Inverse function | Elementary function | Arithmetic overflow | Fresnel integral | GNU Scientific Library | Antiderivative | Continued fraction | Mean | Statistics | Probability | Quantile function | Errors and residuals | With high probability | Entire function | Gaussian integral | Minimax approximation algorithm | Q-function | Faddeeva function | Asymptotic expansion | Bit error rate | Imaginary unit | Extended precision | Hermite polynomials | Maclaurin series | Gaussian function | Arithmetic underflow | Goodwin–Staton integral | Sign function | Sigmoid function | Gamma function | Closed-form expression | Even and odd functions | Incomplete gamma function | Heat equation | Normal distribution | Standard deviation | Complex conjugate | Probit | Random variable | James Whitbread Lee Glaisher | Double factorial | Expected value | Complex number | Integration by parts | Partial differential equation | Dawson function | Heaviside step function | Newton's method | Mittag-Leffler function