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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.

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  • $\begingroup$ Have you tried mathematica or maple? $\endgroup$ – Mhenni Benghorbal Feb 7 '16 at 19:54
  • $\begingroup$ 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... $\endgroup$ – Dac0 Feb 7 '16 at 20:02
  • $\begingroup$ The integral is not elementary! You can have an answer in terms of the error function. See [here] (m.wolframalpha.com/input/…). $\endgroup$ – Mhenni Benghorbal Feb 7 '16 at 20:28
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    $\begingroup$ thank you very much... I was afraid it wasn't plain... $\endgroup$ – Dac0 Feb 7 '16 at 20:40
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    $\begingroup$ I 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... $\endgroup$ – Dac0 Feb 7 '16 at 21:46

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