Show that the Fourier sine series on (0, l) can be derived
Chapter 5, Problem 5.2.5(choose chapter or problem)
Show that the Fourier sine series on (0, l) can be derived from the full Fourierserieson(l,l)asfollows.Let(x)beany(continuous)function on (0, l). Let (x) be its odd extension. Write the full series for (x) on (l,l).[Assumethatitssumis (x).]ByExercise4,thisserieshasonly sine terms. Simply restrict your attention to 0 < x < l to get the sine series for (x).
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