Classic Fourier Series

[Snorre]

Hello Salvo,

a program is always a good idea ;-)

Just two tips:

1st:
You should take care of the argument types your program expects.
Your code seems to expect fun to be an expression (not a function) with t (and only t) being the independent variable, so the typical usage looks like:
fourcoeff(t²,1) or
f(x):=x² and fourcoeff(f(t),1).
By that you have to always remember that fun must be an expression of t. And furthermore, t must not be defined already.
If you change your program slightly by

Code:

...
a0:=int(fun(t),t,0,2*PI)/(2*PI);
ak:=int(fun(t)*cos(k*t),t,0,2*PI)/PI;
bk:=int(fun(t)*sin(k*t),t,0,2*PI)/PI;
...

it'll expect fun to be a function (not an expression) of arity 1. The advantage of this approach is: it doesn't matter how you name the independent variable since your program will replace it by the local t anyway which is totally independent of any global t already defined. That is, you could do something like: t:=["foo","bar"] and g(x):=x² and fourcoeff(g,1).

2nd:
Your program returns a sequence (an object similiar to those created by the builtin seq function), not a vector/list.
That is totally OK as long as it was your intention. Just be aware that sequences behave quite differently when used in further calculations, for example 0+fourcoeff(...) vs. 0+[fourcoeff(...)].
If you want your program to return a vector or list, put the last expression return a0,ak,bk; within brackets or braces: return [a0,ak,bk]; or return {a0,ak,bk};.

Greetings