To show that the eigenfunctions of an eigenvalue problem don't form a complete set, I have to show that there is a function that satisfies the boundary conditions of the problem, but it cannot be written as a linear combination of the functions that consist the set of the eigenfunctions, right?
To find such a function, do I have to look for a square-integrable function?
Or any function that satisfies the problem?
In my notes there is the following sentence:
"For a Sturm-Liouville problem the set of the orthonormal functions $u_1, u_2, u_3, \dots$ is complete, that means that each square-integrable $f$ can be written with a unique way as $f(x)=\sum_{n=1}^{\infty}{c_n u_n(x)}$."
But the problem of my exercise is not a Sturm-Liouville problem.
