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.

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- Jun 6th 2011, 03:53 PMteazyFourier row
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. - Jun 7th 2011, 12:08 AMOpalg
[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 $\displaystyle n\to\infty$).