- #1

- 713

- 5

Sorry, the title should be:

My question is:

does the formula of the moments have a geometrical interpreation?

It is defined as: [tex]m(p) = \int{x^{p}f(x)dx}[/tex]

If you cant see the formula it is here too: http://en.wikipedia.org/wiki/Moment_(mathematics) with c=0.

For example the Fourier series, are computed by inner products of the original function with all the basis functions (which are orthogonal): this means we are essentially finding the projections of the function onto the basis.

For the moments formula, we are computer inner products between the function and the "basis" polynomials 1, x, x^2, x^3, ... which are not always orthogonal.

What's the geometrical meaning of this? if any?

**geometric intepretation of moments**My question is:

does the formula of the moments have a geometrical interpreation?

It is defined as: [tex]m(p) = \int{x^{p}f(x)dx}[/tex]

If you cant see the formula it is here too: http://en.wikipedia.org/wiki/Moment_(mathematics) with c=0.

For example the Fourier series, are computed by inner products of the original function with all the basis functions (which are orthogonal): this means we are essentially finding the projections of the function onto the basis.

For the moments formula, we are computer inner products between the function and the "basis" polynomials 1, x, x^2, x^3, ... which are not always orthogonal.

What's the geometrical meaning of this? if any?

Last edited: