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##### Quiz-5 / Qz5-THREE-E

« Last post by**duoyizhang**on

*March 16, 2021, 01:27:02 AM*»

The question is:Decompose f(x) = xcos(x) into full Fourier series on interval [0, pi].

My confusion is how to decompose it on an interval like [0,𝑙] rather than[-l,l]

Firstly,I compute f(x) into full Fourier series on interval [-pi, pi] by the formula,Which is $$f1=f(x)=-\frac{sinx}{2}+\sum_{n=2}^\infty\frac{2n(-1)^{n}}{n^{2}-1}$$

Then what should we do to compute f(x) on[0,pi],I tried to use the property that f(x)is an odd function but it seems to be wrong.

Any help will be appreciated!

My confusion is how to decompose it on an interval like [0,𝑙] rather than[-l,l]

Firstly,I compute f(x) into full Fourier series on interval [-pi, pi] by the formula,Which is $$f1=f(x)=-\frac{sinx}{2}+\sum_{n=2}^\infty\frac{2n(-1)^{n}}{n^{2}-1}$$

Then what should we do to compute f(x) on[0,pi],I tried to use the property that f(x)is an odd function but it seems to be wrong.

Any help will be appreciated!