I know that this is on the boundaries of what's allowed, but hopefully someone'll answer before it gets closed!


What (periodic) function has Fourier series the harmonic series? I really want the even (cosine) terms to be the harmonic series and no odd terms.


Edit: so that the record is perfectly clear, what I wanted was a function with Fourier series


$$
\sum\_{n \ge 1} \frac{1}{n} \cos(n \pi t)
$$



What function has fourier series the harmonic series?
It's a standard series computation to show that 


$$
\sum\_{n \ge 1} \frac{x^n}{n} = \log \frac{1}{1 - x}
$$


Now substitute $x = e^{i t}$ and take the real part. 


(As an aside, the reason I write the identity this way is that this is the version which is combinatorially significant.)


