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Math Help - Sawtooth function fourier series converge problem

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    Sawtooth function fourier series converge problem

    Sawtooth function fourier series converge problem-qq2.jpg
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  2. #2
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    The Key idea is what each extention represents.

    Cosine is an even extention on (-L,L)

    so f(-x)=f(x) and since a fourier sereis is peroidic and even we get

    f\left(\frac{3}{2}L \right)=f\left( -\frac{L}{2}\right) = f\left( \frac{L}{2}\right)=\frac{L}{2}

    Sine is an odd extention on (-L,L)

    so f(-x)=-f(x) and since a fourier sereis is peroidic and odd we get

    f\left(\frac{3}{2}L \right)=f\left( -\frac{L}{2}\right) = -f\left( \frac{L}{2}\right)=-\frac{L}{2}
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