- #1

Ratpigeon

- 56

- 0

## Homework Statement

Use the Fourier series of

f(x) = { 1 |x|<a

{ 0 a<|x|<[itex]\pi[/itex]

for 0<a<[itex]\pi[/itex]

extended as a 2-Pi periodic function for x [itex]\in[/itex]R

to find

[itex]\sum[/itex] Sin

^{2}(na)/n

^{2}

**2. Homework Equations [/b**

I got that the Fourier series of f(x) was

a/[itex]\pi[/itex]+[itex]\sum[/itex] (2/(m[itex]\pi[/itex]) sin(ma) sin(mx)

I'm not sure what to do. I'm guessing that since its meant to use the Fourier series of f; it should be related to f(a), but f(a) is undefined, and the denominator is wrong...

Could anyone please point me in the right direction?

I got that the Fourier series of f(x) was

a/[itex]\pi[/itex]+[itex]\sum[/itex] (2/(m[itex]\pi[/itex]) sin(ma) sin(mx)

## The Attempt at a Solution

I'm not sure what to do. I'm guessing that since its meant to use the Fourier series of f; it should be related to f(a), but f(a) is undefined, and the denominator is wrong...

Could anyone please point me in the right direction?