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March 5th, 2017, 10:37 AM   #1
ZMD
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Legendre polynomials

Show that the Legendre polynomials form a basis.
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March 5th, 2017, 11:28 AM   #2
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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.
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March 5th, 2017, 12:07 PM   #3
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Can you please give a link of such. @romsek
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March 5th, 2017, 01:23 PM   #4
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Quote:
Originally Posted by ZMD View Post
Can you please give a link of such. @romsek
http://web.mit.edu/18.06/www/Spring09/legendre.pdf
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