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.