Okay you have, (shown below)Originally Posted byparallel

for

This is a strictly monotonic function whose discountinuity points are not replacable, therefore it can be represented as a fourier series.

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The constant term,

Now these intervals the function behaves like,

Thus,

Thus,

.

The same idea of spliting the function on the interval is used to find the sine and cosine coefficients. I just do not want to do that because I know how long these fourier computations can take.