fourier_series omits a_0 for odd functions truncated at limits

[mfripp]

Maybe this is intended behavior? I want to calculate a Fourier series for a simple repeated sawtooth function:

f(x) = x, 0 <= x <= 1; f(x + 1) = f(x)

In sympy, I tried

from sympy import fourier_series
from sympy.abc import x
fourier_series(x, (x, 0, 1)).truncate()

This gives a Fourier series that is missing the a_0 = 1/2 term. When I look at the fourier_series source code, this seems to be because fourier_series identifies the function x as an odd function, so then it only calculates the sine sequence (the b_n terms). However, this skips calculating a_0, which is normally generated along with the cosine sequence.

I can work around this by modifying the function, e.g., this gives expected behavior:

from sympy import fourier_series, Heaviside as u
from sympy.abc import x
fourier_series(x*(u(x)-u(x-1)), (x, 0, 1)).truncate()

But this makes the fourier_series several times slower, because it now has to do integrals with x*(u(x)-u(x-1)) instead of just x. And it seems like this adjustment shouldn't be needed, because the limits already indicate that this is not an odd function.

Is it possible to update fourier_series to check whether the limits are symmetrical at the same time as it checks whether the function is odd? With asymmetrical limits, it should always calculate the a_0 term, even if the function is odd.