Math Help - Normalized Polynomial Coeffients

1. Normalized Polynomial Coeffients

I've been using curve fitting algorithms to derive polynomial coefficients for a given set of data. That works fine. But the problem I am having, is that the device I need to send these coefficients to says they have to be "Normalized Polynomial Coefficients". I've seen the term all over, but nowhere have even seen a definition for what that means, let alone a method for calculating it. Can someone please point me in the right direction to a link or article explaining this? Thank you in advance.

2. I would reckon they mean something like the Legendre Polynomials.

Say we have some vector space we can call $P_{2}$ and its

inner product is $=\int_{-1}^{1}p(x)q(x)dx$

If we use the Gram-Schmidt process to to transform the standard basis,

$[1,x,x^{2}]$, into an orthonormal basis.

The polynomials in the resulting basis are called the Normalized

Legendre Polynomials.

Go ahead and google Legendre Polynomials and you will find plenty.

There is an easy way to find them called Rodrigues's Formula.

Like a unit vector, a normalized function has length 1.