List of integrals of Gaussian functions


In these expressions,
is the standard normal probability density function,
is the corresponding cumulative distribution function and
is Owen's T function.
Owen has an extensive list of Gaussian-type integrals; only a subset is given below.

Indefinite integrals

In these 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.

Definite integrals