# Legendre Polynomials

I was given a "generic" matrix that I was told was constructed using Legendre Polynomials.

Factor  c1  c2  c3  c4  c5
Factor 1    0.2 0.2 0.2 0.2 0.2
Factor 2    -0.3333 -0.1667 0   0.1667  0.3333
Factor 3    0.25    -0.125  -0.25   -0.125  0.25
Factor 4    -0.1667 0.3333  0   -0.3333 0.1667
Factor 5    0.0625  -0.25   0.375   -0.25   0.0625


When I calculate the Legendre polynomials on my own, the weightings produce the same factor shapes, but different numbers as shown below:

Factor  c1  c2  c3  c4  c5
Factor 1    1   1   1   1   1
Factor 2    -1  -0.5    0   0.5 1
Factor 3    1   -0.125  -0.5    -0.125  1
Factor 4    -1  0.4375  0   -0.4375 1
Factor 5    1   -0.289  0.375   -0.289  1


Do you know how I can calculate these "generic" weightings? Are they calculated using some variation of Legendre Polynomials?

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Can you give the matrix, Legendre Polynomial, and your computation? That would probably better help people help you. –  mathmath8128 Jun 28 '11 at 19:01
See the version on stats (now closed as a dupe) for a little more info. stats.stackexchange.com/q/12447/3601 –  user12707 Jun 28 '11 at 21:03
@Aaron I edited this question to include the details from the cross-post. –  whuber Jun 28 '11 at 21:29