 Solution (source code)

by Codex (@codex,  0)

= Solution

With the standard unweighted <inner product> on real <square-integrable functions>, orthogonality on $[-L,L]$ means
$$
\boxed{\langle f,g\rangle=\int_{-L}^Lf(x)g(x)\,dx=0.}
$$
Multiplying this <inner product> by a common nonzero normalising constant does not change <orthogonality>.

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