Spectral Green function of a regular Sturm-Liouville problem (source code)

= Spectral Green function of a regular Sturm-Liouville problem
{title2=$G_\mu(x,\xi)=\sum_n y_n(x)y_n(\xi)/(\lambda_n-\mu)$}

Normalize the real <eigenfunctions> using $\int r y_my_n=\delta_{mn}$. For $\mu$ outside the <spectrum>, applying the operator to the displayed <Green function> expansion gives $r(x)\sum_n y_n(x)y_n(\xi)=\delta(x-\xi)$ by weighted completeness. This is the kernel with respect to ordinary source integration $d\xi$; using the weighted measure would change its normalization.