# fourier

• August 10th 2007, 05:05 AM
kamaksh_ice
fourier
Solve this!!

∞∑n=0 (sin2nө/n!)
• August 10th 2007, 05:24 AM
topsquark
Quote:

Originally Posted by kamaksh_ice
Solve this!!

∞∑n=0 (sin2nө/n!)

I'm very rusty on this, but assume we have a function $f(x)$ such that the Fourier sine series for f is
$F[f(x)] = \sum_{n = 0}^{\infty}\frac{1}{n!}sin(2n \theta)$

Then we need to invert the Fourier sine series, which if I remember correctly means that
$f(x) = \frac{1}{2 \pi} \int_{-\infty}^{\infty} \sum_{n = 0}^{\infty}\frac{1}{n!}sin(2n\theta) sin(x \theta) d \theta$

Someone needs to check me on that result, but it's going to be something of the sort. (The best way for you, kamaksh_ice, to check me is to do the problem then take the Fourier sine series of the result and see if you get your original series back.)

-Dan