Probability Integral

the name of several mutually related special functions. The integral

is called the Gaussian probability integral. For a random quantity X having a normal distribution with an expected value 0 and variance σ², the probability of the inequality ǀXǀ ≤ x is equal to Φ(x/≤. In addition to this, the name “probability integral” is used for the integrals

The latter function is usually designated erf (x) (from “error function”).