> restart;

> plots[setoptions](colour=BLACK);

> FourierSineSeries3 := proc( f, x )
local k, z, F, fop, desc;
desc := sprintf( "Computes Fourier Sine Series of %a", f );
fop := unapply(f,x);
F := 2*int( sin(k*Pi*z)*fop(z), z=0..1 );
subs(DUMMY=desc,proc(n)
local j, s, tmp;
option Copyright;
description DUMMY;
s := 0;
for j to n do
try
tmp := eval( F, k=j );
catch "numeric exception: division by zero":
tmp := limit( F, k=j );
finally
s := s + tmp*sin(j*Pi*x);
end try;
end do;
end proc);
end proc:

> macro( FSS3=FourierSineSeries3 );

> f := FSS3( x^2*(1-x^2), x );

> read "D:/books/ess/programs/fouriersine.mpl";

> macro( FSS=FourierSineSeries );

> f1 := FSS( x*sin(Pi*x), x );

> f1( 10 );

Error, (in c) numeric exception: division by zero

> f3 := FSS3( x*sin(Pi*x), x );

> int( sin(Pi*k*x)*x*sin(Pi*x), x=0..1 );

> bad := FSS( x*sin(Pi*x)^2, x );

> bad( 10 );

Error, (in c) numeric exception: division by zero

> good := FSS3( x*sin(Pi*x)^2, x );