The error function, also called the Gauss error function and often denoted erf, is defined by a definite integral of the exponential of negative t squared, scaled so its value approaches 1 as its argument grows large. It is a nonelementary, sigmoid-shaped function that occurs often in probability, statistics, and partial differential equations; for a normally distributed real random variable with mean 0 and standard deviation one over the square root of two, the error function gives the probability that the variable falls within a given symmetric range around zero. Two closely related functions are the complementary error function, equal to one minus the error function, and the imaginary error function.
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Glaisher in 1871 on account of its connection with "the theory of probability, and notably the theory of errors".
Introduction, second paragraph
This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations.
In Branch: Probability and Statistics, Lead paragraph
This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations.
Attributed To: Carl Friedrich Gauss, Lead section
the error function (also called the Gauss error function)
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