Gaussian Integrals

(edited by Roberto Bigoni)


The integrals of the form

Eqn001.gif

which are frequently encountered in the probability theory, considered as functions of a, have the following recursive property

Eqn002.gif

that is

Eqn003.gif

Therefore, if we know Io(a) and I1(a), we can calculate any other In(a).

Finally we can obtain from (2)

Eqn013.gif

and so on.

 

In general

Eqn014.gif

that is

Eqn015.gif


last revision: May 2018