Fourier Series of a constant (Pi)?

[Major_Disaster]

Homework Statement

Determine the Fourier series of f(x) = pi + x

Homework Equations

The Attempt at a Solution

I see you have to calculate the two "series" separately and then add them. I know that the Fourier series of pi is just pi - but i was wondering why (i know that sounds ridicolous).

Is it simply a case of, pi is not perioidic so can't be expanded as a Fourier series so its just pi?

Or can you (as i have been trying and failing to do), somehow plug into the Fourier equations (for bn) show that the series is zero, but the a0 is 2pi, so its just pi?

Just interested is all...

Thanks

 

[eok20]

The Fourier transform of a constant is that constants times the delta function, which is not really a function but a distribution (I'm assuming you're working over all of R).

 

[vela]

Homework Statement

Determine the Fourier series of f(x) = pi + x

The Attempt at a Solution

I see you have to calculate the two "series" separately and then add them.

You don't have to calculate them separately.

I know that the Fourier series of pi is just pi - but i was wondering why (i know that sounds ridicolous).

Is it simply a case of, pi is not perioidic so can't be expanded as a Fourier series so its just pi?

A constant function f(x)=c is periodic because f(x)=c=f(x+T).

Or can you (as i have been trying and failing to do), somehow plug into the Fourier equations (for bn) show that the series is zero, but the a0 is 2pi, so its just pi?

Just interested is all...

Thanks

Yes, that's exactly what you do.