March 5th, 2017, 10:37 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 48 Thanks: 0  Legendre polynomials
Show that the Legendre polynomials form a basis.

March 5th, 2017, 11:28 AM  #2 
Senior Member Joined: Sep 2015 From: CA Posts: 1,238 Thanks: 637 
use the fact that the LPs are obtained by performing GramSchmidt orthogonalization on the basis $\{1,~x,~x^2,~\dots, ~x^n\}$ since that basis clearly spans polynomials of degree $n$ and the GS process doesn't alter the span of the original basis the LPs will span it as well. There are a variety of places online where this is done in detail. 
March 5th, 2017, 12:07 PM  #3 
Member Joined: Nov 2016 From: Kansas Posts: 48 Thanks: 0 
Can you please give a link of such. @romsek

March 5th, 2017, 01:23 PM  #4 
Senior Member Joined: Sep 2015 From: CA Posts: 1,238 Thanks: 637  

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legendre, numerical analysis, polynomials 
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