March 5th, 2017, 09:37 AM  #1 
Member Joined: Nov 2016 From: Kansas Posts: 55 Thanks: 0  Legendre polynomials
Show that the Legendre polynomials form a basis.

March 5th, 2017, 10:28 AM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,493 Thanks: 752 
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, 11:07 AM  #3 
Member Joined: Nov 2016 From: Kansas Posts: 55 Thanks: 0 
Can you please give a link of such. @romsek

March 5th, 2017, 12:23 PM  #4 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,493 Thanks: 752  

Tags 
legendre, numerical analysis, polynomials 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Hankel transform  Legendre polynomials  tsam  Calculus  0  December 3rd, 2016 01:42 AM 
A connection between Gegenbauer and Legendre polynomials  avniu  Algebra  0  August 15th, 2016 09:56 AM 
research about legendre polynomials  ruba.math  Applied Math  0  September 13th, 2013 04:54 AM 
Integral of Legendre polynomials  JiriV  Calculus  1  April 30th, 2013 07:27 AM 
Legendre function  mathbalarka  Calculus  1  April 25th, 2012 06:25 AM 