I would need to find the fourier coefficient of this gaussian for a problem. I'm now stuck with this integral, \begin{equation} c_{n}=\int_{-1}^{1}e^{\frac{x^{2}}{2}}\left(\cos\left(\pi nx\right)\right)dx. \end{equation} I'm not sure if it is possible an analytical solution, does anybody know? Please note that's on an interval and not on the whole line.
Asked
Active
Viewed 593 times
1
-
Have you tried mathematica or maple? – Mhenni Benghorbal Feb 07 '16 at 19:54
-
I'm not really good at neither... any way I would like to know if it exists a way for solving it analytically before switching to numerically... – Dac0 Feb 07 '16 at 20:02
-
The integral is not elementary! You can have an answer in terms of the error function. See [here] (http://m.wolframalpha.com/input/?i=Int%28exp%28x%5E2%2F2%29cos%28+n%5Cpi+x%29%2C+x%3D-1..+1%29&x=12&y=7). – Mhenni Benghorbal Feb 07 '16 at 20:28
-
1thank you very much... I was afraid it wasn't plain... – Dac0 Feb 07 '16 at 20:40
-
You are very welcome! By the way where did this problem come from? – Mhenni Benghorbal Feb 07 '16 at 21:21
-
1I was trying to find an function that could be easy to write in Fourier Expansion and Hermite Expansion at the same time, maybe I could ask this question directly... – Dac0 Feb 07 '16 at 21:46
-
Here is a useful integral for you – Mhenni Benghorbal Feb 07 '16 at 21:57