Orthogonal polynomials for the absolute-value weight
= Orthogonal polynomials for the absolute-value weight
{title2=$\phi_0=1,\quad\phi_1=x,\quad\phi_2=x^2-\tfrac12$}
For the <inner product> obtained by integrating with weight $|x|$ on $[-1,1]$, odd moments vanish and the moment of $x^{2m}$ is $1/(m+1)$. The first <monic orthogonal polynomials> are $1$, $x$ and $x^2-1/2$. <Positive definiteness> follows because the weight is positive <almost everywhere> and a nonzero <polynomial> cannot vanish <almost everywhere>.