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mathletic · May 21, 2014, 05:54 AM

I am solving an initial-boundary value problem and I got to a point that I have to calculate the coefficients knowing that:
x=Σ{A_n sin(((2n+1) π x)/(2L))}

One way to calculate the coefficient is the Fourier series, isn't it?

So I thought the following:

We expand the function f(x)=x in an odd way at [-L,L].

So we can write the function as a Fourier series.

Can we write it as followed?

f(x)=Σ{b_nsin((2(2n+1) π x)/(2 * 2L))},
where b_n= 2/(4L) ∫_{-L}^L{f(x) sin((2 (2n+1) π x)/(4L))}dx

Or can we not do this in this way?

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