Let f be extended into (L, 2L] in an arbitrary manner
Chapter 10, Problem 38(choose chapter or problem)
Let f be extended into (L, 2L] in an arbitrary manner subject to the continuity conditionsofTheorem 10.3.1.Then extend the resulting function into (2L, 0) as an odd function andelsewhere as a periodic function of period 4L (see Figure 10.4.6). Show that this functionhas a Fourier sine series in terms of the functions sin(nx/2L), n = 1, 2, 3, ... ; that is,f(x) = n=1bn sin(nx/2L),wherebn = 1L2L0f(x)sin(nx/2L) dx.This series converges to the original function on (0, L).
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