I need to decide whether this trigonometrial row
\Sum_{n=-25}^{50} (n^3+1)e^(I*n*x)
is a Fourier row for a continous 2\pi periodic function?
I dont know what to do when the row doesnt go from -\infty till \infty??
Thanks for the help.
[Note: the English word used here is series, not row.]
The above expression is a finite sum of continuous $\displaystyle 2\pi$-periodic functions $\displaystyle (n^3+1)e^{inx}$, and is therefore continuous and $\displaystyle 2\pi$-periodic. It would not be possible to extend this particular series to an infinite trigonometric series $\displaystyle \sum_{n=-\infty}^\infty (n^3+1)e^{inx}$ because that series does not converge (the terms become unboundedly large as $\displaystyle n\to\infty$).