# Toronto Math Forum

## APM346-2021S => APM346--Tests & Quizzes => Quiz-5 => Topic started by: duoyizhang on March 16, 2021, 01:27:02 AM

Title: Qz5-THREE-E
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!