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I am trying to find Exponential Fourier series coefficients for a periodic parabolic function

$$ f(t) = t^2, \quad -\pi \le t \le \pi $$

using derivative property of Fourier series. As otherwise, it's a bit tedious to go and compute FS coefficients by integrating them through formula we have for Fourier series coefficients.

The results I am getting is incorrect (I am differentiating parabolic function thrice to get two impulse trains, FS coefficients for impulse trains are $1/T$ and then applying derivative rule), FS coefficients that we must be getting should be purely real and even but I am getting them as purely imaginary. Can someone please correct me where I am wrong.

Thanks a lot!!

Dylan
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ritvik rathore
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    It's hard to tell you where you are going wrong unless you edit your question to show us your calculations. Please see the MathJax basic tutorial and reference if you need help on how to enter maths on this site. –  Jun 14 '18 at 05:35
  • I totally understand but unfortunately I am not allowed to upload picture of my approach here as getting error that I must be having atleast 10 reputation to post images :( . – ritvik rathore Jun 14 '18 at 06:39

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