# Fourier series representation of even and odd functions

I'm not sure where to begin on showing that a Fourier series of a periodic function that is neither odd or even can be represented by the sum of the cosine fourier series and sine fourier series.

I know that an even function of period $2L$ is a Fourier cosine series and simiarly with an odd function and sine series. And that a real valued function can be shown to be the sum of an odd function and an even function. Is this little description enough to show it? Suggestions would be great.

• Yes, that's enough. – Brian Rushton May 31 '13 at 3:35

All of this feels as an unsatisfactory answer, because it is not clear what is a meant by a function here (continuous, an element of $L^2$, etc), and what is the expected level of rigour.