In the expressions in this article,
is the standard normal probability density function,
is the corresponding cumulative distribution function (where erf is the error function), and
Owen[1] has an extensive list of Gaussian-type integrals; only a subset is given below.
In the previous two integrals, n!! is the double factorial: for even n it is equal to the product of all even numbers from 2 to n, and for odd n it is the product of all odd numbers from 1 to n; additionally it is assumed that 0!! = (−1)!! = 1.