Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Geometric intepretation of Taylor series

  1. Apr 26, 2009 #1
    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: [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: Apr 26, 2009
  2. jcsd
  3. Apr 26, 2009 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    What does this have to do with Taylor series?
  4. Apr 26, 2009 #3
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Geometric intepretation of Taylor series
  1. Geometric series (Replies: 2)

  2. Taylor series (Replies: 7)

  3. Taylor series (Replies: 5)