Gauss's probability integral | Gaussian probability integral

The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over (-∞, ∞). It can be computed using the trick of combining two one-dimensional Gaussians integral_(-∞)^∞ e^(-x^2) d x | = | sqrt(( integral_(-∞)^∞ e^(-x^2) d x)( integral_(-∞)^∞ e^(-x^2) d x)) | = | sqrt(( integral_(-∞)^∞ e^(-y^2) d y)( integral_(-∞)^∞ e^(-x^2) d x)) | = | sqrt( integral_(-∞)^∞ integral_(-∞)^∞ e^(-(x^2 + y^2)) d y d x).

erf | Gaussian function | Gauss integral | Leibniz integral rule | normal distribution