question about fourier coefficients I am having trouble showing the following and i was wondering if anyone can point out my mistake.
let f be a 2pi periodic function and 
$$f_m(t)=f(mt)$$
show the n-th fourier coefficient 
$$\hat{f_m}(n)=\hat{f}(n/m)$$ if m divides n
$$\hat{f_m}(n)=0$$ if m does not divides n
my attempt:
$$\hat{f_m}(n)=\frac{1}{2\pi}\int_0^{2\pi}f(mt)e^{-int}dt$$
substitute x=mt we get 
$$=\frac{1}{2\pi}\int_0^{2\pi}f(x)e^{-i\frac{n}{m}x}\frac{dx}{m}$$
as you can see, im having a extra m on the denominator. Furthermore, i do not see why it should equal 0 if m does not divide n

You forgot to substitute the integral limits. Also I think your description of the problem is missing some premise -- is $f$ periodic with period $2\pi$?
