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First of all sorry for my stupidity. I am learning to find Fourier Series coefficient as fast a possible for my exam. But it's getting really confusing deriving a factor.

For example: In one website, I see the formula derived for $a_0$:

Derived Formula 1

On the other hand, I see the formula derived for $a_0$:

Derived Formula 2

Where both function are of the period $2\pi$ and on interval $\left\[-\pi, \pi\right\]$.

It would be really appreciable, if somebody would explain me how the factor in one formula is $1/\pi$ and $1/2\pi$ in another one.

A. Goodier
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Mani Rai
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1 Answers1

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Essentially they are both equivalent. It's just that some literature defines a Fourier series $S(x)$ by

$$S(x)=\frac{a_0}{2}+...$$

and other literature defines it as$$S(x)=a_0+...$$

thesmallprint
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  • Thank you so much... Is it possible to explain me here, how can I find this factor accurately? If not, can you give me a good reference to look at. – Mani Rai Dec 16 '17 at 15:54
  • Just make a choice on how you define a Fourier series and use the relevant formula. If you use the first expression that I put then use the picture associated with "Derived Formula 2" and if you choose the second expression then use the picture associated with "Derived Formula 1". – thesmallprint Dec 16 '17 at 16:02