The term error function has two common mathematical uses. In the theory of special functions, it denotes erf, the entire
function defined for a complex number 
by
This function occurs in integrals
involving the normal distribution.
In optimization theory, an error function can instead mean an objective function to be
minimized. In this usage, it is often also called a loss
function (Goodfellow et al. 2016, p. 80).
See also
Erf,
Loss Function,
Objective Function
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References
Goodfellow, I.; Bengio, Y.; and Courville, A. Deep Learning. Cambridge, MA: MIT Press, p. 80, 2016. https://www.deeplearningbook.org/contents/numerical.html.National
Institute of Standards and Technology. "Error Functions" and "Statistics."
§§7.2(i) and 7.20(iii) in NIST Digital Library of Mathematical Functions.
https://dlmf.nist.gov/7.2.i. https://dlmf.nist.gov/7.20.iii.Referenced
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Error Function
Cite this as:
Weisstein, Eric W. "Error Function." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ErrorFunction.html
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