- #1

- 56

- 0

## Homework Statement

show coth([itex]\pi[/itex])=1/[itex]\pi[/itex] (1+2 [itex]\sum[/itex]

^{[itex]\infty[/itex]}

_{n=1}(1/(1+n^2)

## Homework Equations

The fourier expansion of e^x is

Sinh([itex]\pi[/itex])/[itex]\pi[/itex](1+[itex]\sum[/itex] 2(-1)^m/(1+n^2) (cos(mx)-n sin(nx)

## The Attempt at a Solution

I subbed in

Coth(Pi)=1+e^-pi/sinh(pi) =1+1/[itex]\pi[/itex] (1+2 [itex]\sum[/itex]

^{[itex]\infty[/itex]}

_{n=1}(1/(1+n^2)

But this is wrong because of the one out the front - I know that needs to stay there, which means I somehow need to stick a -sinh(pi) into the front of my fourier series of e^pi I would say that it would be my term for n= zero, but I already took care of that one, which was sinh(pi)/pi...

Please help - I've spent about fifteen pages on the algebra for this and I'm getting really sick of the stupid question...