Explicit closed-form expression for eigenfunction norms (Q5938958)

It is well known that the solution to parabolic or hyperbolic problems for PDEs on a compact can be found (in many cases) in terms of a Frobenius series. This series is due to the eigenfunctions and eigenvalues of the corresponding Sturm-Liouville problem. Here, the author presents a formula that allows explicitly to find the eigenfunction norm for linear second-order Sturm-Liouville problems. Using this formula the author simplifies the exact solutions to second-order parabolic or hyperbolic PDEs.