weight function (Sturm-Liouville)

The function sigma(x) multiplying lambda*y in a Sturm-Liouville equation, which the eigenfunctions turn out to be orthogonal with respect to.

The weight function $\sigma(x)$ in a Sturm-Liouville equation $\dfrac{d}{dx}[p(x)y']+q(x)y+\lambda\sigma(x)y=0$ multiplies the eigenvalue term; it is required to be continuous and strictly positive on $[a,b]$ , and it is exactly the function that has to appear inside the integral for the problem's eigenfunctions to be orthogonal.