// bn's

t = -%pi:0.05:%pi;
[n, m] = size(t);

function y = f(t)
	y = (%pi-t)/2;
endfunction;

n = 10; b=zeros(1,n); for i=1:n, b(i)=(1/%pi)*integrate('f(x)*sin(i*x)','x',0,2*%pi,0.0000001); end;

for i=1:n, printf("1/b[%d] = %f\n", i, 1/b(i)); end;

p=zeros(n,m);
for j=1:m, p(1,j) = b(1)*sin(t(j)); end;
for i=2:n, for j=1:m, p(i,j) = p(i-1,j)+b(i)*sin(i*t(j)); end; end;
clf();
plot(t,p)
g=zeros(t); for j = 1:m, if t(j) < 0 then g(j) = f(t(j)+2*%pi); else g(j) = f(t(j)); end; end;
plot(t,g,"k-")