Geometric intepretation of Taylor series

[mnb96]

Sorry, the title should be: geometric intepretation of moments

My question is:
does the formula of the moments have a geometrical interpreation?
It is defined as: $$m(p) = \int{x^{p}f(x)dx}$$
If you can't 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?

 

[matt grime]

What does this have to do with Taylor series?

 

[mnb96]

Nothing indeed!
I was a bit distracted while I was writing the title, and then I was unable to correct it.
Apparently you were no less distracted than I was, since you didn't seem to notice what I wrote in boldface :)

Sorry, the title should have been: geometric intepretation of moments.