# Gram-Schmidt orthonormalization with polynomials

I'm doing Gram-Schmidt orthonormalization on a sequence of polynomials on $\mathbb{R}[x]$ with $\tau(f,g) = \int_0^\infty f(x)g(x)e^{-x} dx$ and I've got down to a sequence of orthogonal polynomials using the Gram-Schmidt orthonormalization process which are \begin{align*}f_0 &= 1\\ f_1 &= x - 1\\ f_2 &= x^2 - 4x + 2\end{align*} (we only have to do three) but how do you make each of these orthonormal rather than just orthogonal?

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Divide each of them by its norm, $\sqrt{\tau(f,f)}$; that is, multiply by the scalar $\frac{1}{\lVert f\rVert}$. – Arturo Magidin Apr 7 '12 at 16:24
On that note: Your $f_k(x)$ are what are called Laguerre polynomials. – J. M. Apr 27 '12 at 13:38