
#1
Apr2609, 04:34 AM

P: 625

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? 



#2
Apr2609, 05:28 AM

Sci Advisor
HW Helper
P: 9,398

What does this have to do with Taylor series?




#3
Apr2609, 07:28 AM

P: 625

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. 


Register to reply 
Related Discussions  
power series vs. taylor series  Calculus & Beyond Homework  1  
Power Series/Taylor Series  Calculus & Beyond Homework  6  
Taylor series  General Math  4  
Power series & Taylor series  Calculus & Beyond Homework  4  
geometric series/geometric progression  Precalculus Mathematics Homework  2 