Fourier Series: Part (2)pic.twitter.com/M4wvRCl6VF
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(2) In equations (3) and (4) you will notice I replaced an equality that had the index "m" with an equality which had the index "n". This is permitted, since the relation was shown for all m, hence it's also true for m=n.
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(3) Example: If f(x) is a square wave, then the result looks like this. As you can see, the more terms we keep in the series, the better the square wave is approximated by the the Fourier Series.pic.twitter.com/i2FXLmIYDy
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Question..when are the conditions met to have that added a0/2 factor?
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it's worth pointing out that because the function has a jump discontinuity the convergence is pointwise (at any specific point x the series converges to the function) but not uniform (if you always pick the worst point in the series you can stay away from the function)
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