Fourier Example

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Revision as of 01:36, 19 January 2010 by Jorge.cruz (talk | contribs) (Solution)
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Find the Fourier Series of the function:


f(x)={0,πx<0π,0xπ


Solution


Here we have



ao=12π(π00dx+0ππdx)=π2


an=0ππcos(nx)dx=0,n1,


and


bn=0ππsin(nx)dx=1n(1cos(xπ))=1n(1(1)n)


We obtain b2n = 0 and


b2n+1=22n+1


Therefore, the Fourier series of f(x) is

f(x)=π2+2(sin(x)+sin(3x)3+sin(5x)5+...)

References:

Fourier Series: Basic Results