>	# FOURIER SINE SERIES OF A SQUARE WAVE

>

>	# f(x) = 1 on (0,Pi); f(x) = -1 on (-Pi,0); f has period 2*Pi.

>

>	# First we need to calculate the Fourier coefficients.

>	bn := (2/Pi)*Int(sin(n*x), x=0..Pi);

>

value(%);

>	# This is 0 unless n is odd.

>

>	# Note that, unlike the coefficients of the triangle wave, these decrease like 1/n, not 1/n^2.

>

>	bodd := k -> (4/Pi)*(1/(2*k+1));

>	partialsum := K -> sum(bodd(k)*sin((2*k+1)*x), k=0..K);

>	plot(partialsum(0), x=-8..8);

>	plot(partialsum(1), x=-8..8);

>	plot(partialsum(2), x=-8..8);

>	plot(partialsum(4), x=-8..8);

>	plot(partialsum(8), x=-8..8);

>	plot(partialsum(16), x=-8..8);

>	# Let's look up close.

>	plot(partialsum(16), x=-1..4);

>	plot(partialsum(32), x=-1..4);

>	plot(partialsum(64), x=-1..4);

>

>