Checking your Fourier Series coefficients

[WolfOfTheSteps]

When you compute the Fourier series coefficients for a function, is there any quick way to check if your answer is correct or at least reasonable?Thanks.

 

[christianjb]

I would graph it using plotting software.

You could also pick a random value of x and calculate the first few terms by hand.

 

[WolfOfTheSteps]

So I guess that means there is no quick way to tell, when you are taking a test or something?

 

[christianjb]

It's a good question. Maybe someone else can give you better advice.

 

[Gib Z]

There is not really an easy shortcut, but one thing you could do is Check that $$f(0)= \left( \sum_{n=0}^{\infty} a_n \right) - \frac{a_0}{2}$$

That only checks your a_n, for b_n all I can offer is to recheck your derivation. Good Luck lol