I just calculated the Fourier series of x^2-(pi^2)/2 and noticed, that it's no different from the Fourier series of x^2, except for the a_0. Is that just a coincidence, or can i simply use the Fourier series of the known function and then simply calculate the according a_0?

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I just calculated the Fourier series of x^2-(pi^2)/2 and noticed, that it's no different from the Fourier series of x^2, except for the a_0. Is that just a coincidence, or can i simply use the Fourier series of the known function and then simply calculate the according a_0?

Mathematics
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a_0 is the only constant term in a Fourier series. Hence of you have the Fourier series of f(x), you can calculate immediately the Fourier series of g(x) = f(x) + c by modifying the a_0 term of the Fourier series of f(x)
That will be pretty useful at the exam, thank you :)

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