Shifted Legendre Polynomial

Hi:

I'm kinda confused about Legendre Polynomial.

SO if i was to calculate the orthogonal polynomials int eh interval [0,1]

can't i do soemthing like this:


p0 = 1
p1 = x - c0 p0

such that Integral p0p1 over the interval [0, 1] shd be zero. After solving for p1 I get

c0 = 1/2
p1 = x - 1/2


but the actual shifted legendre polynomial for p1 = (1-2t)

I don't understand as to how to calculate orthonormal/orthogonal polynomials in a particular interval. I'd really appreciate if someone could explain me the subtleties of the gram-schmidt.

See here, starting at around post 36, for an example of Gram-Schmidt on polynomials. The inner product is different, but the idea is the same.

Thanks for trying to help. I went through it, but I still don't understand. Can you tell em what the difference is in the example that I gave and if it looks right and maybe explain the difference. I'm sorry to bother you like this, but I have been struggling to understand this since morning. I'dk which one seems right. And this ties to all the other problem I'm having with interval shift in case of chebyshev, GS.

Thanks!

Please look here
Legendre polynomials - Wikipedia, the free encyclopedia

The interval is (-1, 1).