Toronto Math Forum
APM3462021S => APM346Tests & Quizzes => Quiz5 => Topic started 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!