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 March 5th, 2017, 10:37 AM #1 Newbie   Joined: Nov 2016 From: Kansas Posts: 25 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: 898 Thanks: 483 use the fact that the LPs are obtained by performing Gram-Schmidt 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 Newbie   Joined: Nov 2016 From: Kansas Posts: 25 Thanks: 0 Can you please give a link of such. @romsek
March 5th, 2017, 01:23 PM   #4
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Joined: Sep 2015
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Quote:
 Originally Posted by ZMD Can you please give a link of such. @romsek
http://web.mit.edu/18.06/www/Spring09/legendre.pdf

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