# Thread: How to be sure that a serie isn't a fourier series of a derivable function

1. ## How to be sure that a serie isn't a fourier series of a derivable function

Hi there. I have this interesting problem which I don't know how to solve. I'll post it here because I think more people will se it, but I'm not sure if this is the proper subforum.

The problem says: How can be sure that $\displaystyle \sum_{n = 1}^\infty \frac{1}{n}\sin (nx)$ isn't the Fourier series of a derivable function?

I thought that it doesn't accomplish the Diritchlet postulates, but it actually doesn't mean that it isn't a fourier series.

Does anyone know how to solve this?

Bye there and thanks.

2. If $\displaystyle f$ is the function which is represented by this series and derivable, use an integration by parts to compute the Fourier coefficients of $\displaystyle f'$. Use Parseval equality to show a contradiction.

3. Originally Posted by Ulysses
...Fourier series of a derivable function?...
A better phrase would be "differentiable function", just for your information.