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Probability Integral

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ProbabilityIntegralReal
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ProbabilityIntegralReImAbs
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alpha(x)=1/(sqrt(2pi))int_(-x)^xe^(-t^2/2)dt
(1)
=sqrt(2/pi)int_0^xe^(-t^2/2)dt
(2)
=2Phi(x)
(3)
=erf(x/(sqrt(2))),
(4)

where Phi(x) is the normal distribution function and erf is the error function.

See also

Erf, Normal Distribution Function

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Cite this as:

Weisstein, Eric W. "Probability Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProbabilityIntegral.html

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