AngouriMath
Navigation
← Back to list of members
GaussianMoment(AngouriMath.Entity,AngouriMath.Entity.Variable)
Method (no overloads)
Summary
int k x^m F^(a x^2 + c) dx for a whole m, not zero, and a non-zero a: the
Gaussian moments. With A = a ln F and I_m the integral of
x^m e^(A x^2), parts give I_m = x^(m - 1) e^(A x^2)/(2A) - (m - 1)/(2A) I_(m - 2),
and read the other way I_m = x^(m + 1) e^(A x^2)/(m + 1) - 2A/(m + 1) I_(m + 2) for a
negative m, each two powers nearer the Gaussian I_0. An odd positive m ends at I_1 = e^(A x^2)/(2A), which is elementary and answered elsewhere, and an odd
negative one at I_(-1) = Ei(A x^2)/2.
https://github.com/asc-community/AngouriMath/issues/1501
Angouri © 2019-2023 ·
Project's repo ·
Site's repo ·
Octicons ·
Transparency ·
4378 pages online