I have the following expression:
$\displaystyle -\frac{1}{4}\cdot\frac{(-2+n\cdot sin(\pi n)\pi + 2cos(\pi n))\cdot sin(nx)}{n^3}$
I need to rewrite it and end up with:
$\displaystyle \frac{sin((2n-1)t)}{(2n-1)^3}$
I have the following expression:
$\displaystyle -\frac{1}{4}\cdot\frac{(-2+n\cdot sin(\pi n)\pi + 2cos(\pi n))\cdot sin(nx)}{n^3}$
I need to rewrite it and end up with:
$\displaystyle \frac{sin((2n-1)t)}{(2n-1)^3}$
Nevermind, I figured it out on my own.
It's part of a fourier series. I found out that for all $\displaystyle n=even$ the expression will yield zero and for all $\displaystyle n=uneven$ the expression will yield $\displaystyle \frac{sin(nt)}{n^3}$
For $\displaystyle n$ expressed as an uneven integer, we can rewrite it as $\displaystyle n=2k-1$ thus if you insert this and change $\displaystyle k$ to $\displaystyle n$ in the new expression, the work is then complete. Sorry for not writtign my question that good, my bad.