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
is Owen's T function.
Owen. has an extensive list of Gaussian-type integrals; only a subset is given below.
Indefinite integrals
lists this integral without the minus sign, which is an error. See calculation by WolframAlpha.
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 .
report this integral with error, see WolframAlpha.
Definite integrals
report this integral incorrectly by omitting x from the integrand.
References