List of integrals of Gaussian functions


In the expressions in this article,
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 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.
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