1. Prove that if f(x) is continous in R with a period of 2pi and hjer fourier coefficients are 0 then
f(x)=0. Deduce that two different continous functions in R with a period of 2pi has different fourier series..
2. Prove by finding the fourier series at (0,pi) that for every x in (0,pi):
cosx= 8/pi * Sigma [ (n*sin(2nx) ) / (4n^2 - 1) ]. Check if the formula is correct for x=0 and x=pi and explain why the series doesn't uniformly converges at (0,pi). Is it pointwise converge at (0,pi)? Mean converges?
The Attempt at a Solution
I've no idea how to solve it...I'm pretty lame at this and have no idea what to do... I'll be glad to recieve some detailed guidance...
Thanks in advance