# Fourier series

1. May 11, 2008

### gtfitzpatrick

1. The problem statement, all variables and given/known data

if 0<$$\lambda$$<1 and
f(x) = x for 0<x<$$\lambda\pi$$ and
f(x) = ($$\lambda$$/(1-$$\lambda$$))($$\pi$$-x) for $$\lambda\pi$$<x<$$\pi$$

show that f(x)= 2/($$\pi$$(1-$$\lambda$$))$$\Sigma$$(sin( n$$\lambda$$$$\pi$$)sin(nx)(/n$$^{}2$$

2. Relevant equations

3. The attempt at a solution
am i right in saying that there is only odd so ao = 0 and an = 0

and bn = 2/$$\pi$$ ($$\int^{\lambda\pi}_{0}$$ x + $$\int^{\pi}_{\lambda\pi}$$ of the second part) sin(nx)