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 has an extensive list of Gaussian-type integrals; only a subset is given below.
In the previous two integrals, is the double factorial: for even it is equal to the product of all even numbers from 2 to , and for odd it is the product of all odd numbers from 1 to ; additionally it is assumed that .