# [Maxima] fourie package behavior

Edwin Woollett woollett at charter.net
Sat Sep 13 15:43:13 CDT 2008

```>On Sept. 13, 2008, Edwin Woollett wrote
>If we use the calculus/fourie.mac package
>to find the fourier series coefficients
>of the function f(x) = x over the
>interval (-pi, pi), we can use foursin(...),
>the sign of cos(%pi*n), where "n" is
>a local variable assumed positive inside
>foursin(...). The correct set of coefficients

foursin(..) calls a locally defined function
called adefint(..), which, for this case,
then calls ldefint(...) which is where this
question is coming from:

(%i16) ldefint( x*sin(n*x), x, 0, %pi );
Is  cos(%pi*n)  positive, negative, or zero?
p;
(%o16) sin( %pi*n )/n^2 - %pi*cos( %pi*n )/n

(%i17) ldefint( x*sin(n*x), x, 0, %pi );
Is  cos(%pi*n)  positive, negative, or zero?
n;
(%o17) sin( %pi*n )/n^2 - %pi*cos( %pi*n )/n

(%i18) ldefint( x*sin(n*x), x, 0, %pi );
Is  cos(%pi*n)  positive, negative, or zero?
z;
(%o18) sin( %pi*n )/n^2 - %pi*cos( %pi*n )/n

ldefint(..) apparently "needs" the sign of something,
but if any answer will do, then it doesn't really
"need" it (??).

Ted Woollett

```