f(x)
The function definition should be given as an array.
[ [f(t₁), t₁, t₂] , [f(t₂), t₂, t₃] , ...[f(t_n), t_n, t_n+1] ]

Where...
f(t₁) is the function definition for t₁ < t < t₂
f(t₂) is the function definition for t₂ < t < t₃

Total period of the function is given by [ t_n+1 - t₁ ]

[n]
This parameter indicates what to return.
n > 0 returns the indicated number of coefficients (from 0 to n for trigonometric series and from -n to +n for complex form).
n <= 0 returns only the single coefficient with number n (or +n and -n for complex form).
non-number returns a general formula for the given function (trigonometric or complex). This formula is not always the simplest form.

[mode]
This optional paramter indicates if the result should be given as a trigonometric series or in complex form.
mode = 0 returns trigonometric series. This is the default mode.
mode = 1 returns the complex form.


Description
Creates the Fourier series of a given function.

Examples

FourierSeries([[-1, -\pi, 0], [1, 0, \pi]], x, 8)

FourierSeries([[-x, -\pi, 0], [1, 0, \pi]], x, 6)

FourierSeries([[0, -\pi, 0], [\pi, 0, \pi]], x, 10)

FourierSeries([[-cos(z), -\pi, 0], [cos(z), 0, \pi]], z, 10)

FourierSeries([[-1, -\pi, 0], [1, 0, \pi]], x, 6, 1)

FourierSeries([[-x, -\pi, 0], [x, 0, \pi]], x, 6, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, 6, 1)

FourierSeries([[cos(z), -\pi/2, \pi/2], [0, \pi/2, 3\pi/2]], z, 6, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, 0, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -1, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -2, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -3, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -4, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -5, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, 0, 0)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -1, 0)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -2, 0)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -3, 0)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -4, 0)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, -5, 0)

FourierSeries([[-1, \pi, 0], [1, 0, \pi]], x, f, 1)

FourierSeries([[sin(z), 0, \pi], [0, \pi, 2\pi]], z, f, 1)

Plot(FourierSeries([[-1, -\pi, 0], [1, 0, \pi]], x, 20), color=red)

Plot(FourierSeries([[-x, -\pi, 0], [x, 0, \pi]], x, 10), color=blue)

Plot(FourierSeries([x, -\pi, \pi], x, 20), color=purple)

Plot(FourierSeries([x*(\pi-x)(\pi+x), -\pi, \pi], x, 10), color=red)

Plot(FourierSeries([[0, -\pi, 0], [\pi, 0, \pi]], x, 20), color=orange)

Plot(FourierSeries([x^2, -\pi, \pi], x, 20), color=blue)

References

http://mathworld.wolfram.com/FourierSeries.html

http://en.wikipedia.org/wiki/Fourier_series

Related Functions
FourierSin, FourierCos