>
> I tried to calculate the integral of
> sinc(x)
> sinc(x)*sinc(x/3)
> ...
> over x=0..%plusInfinity, and the second one already gave the answer
> "Failed".
> However, Fricas can calculate the primitive function,
<snip>
> but not its limit at infinity (again "Failed").
> It can calculate the limit of all the summands:
>
> (18) -> limit(12*cos(x/3)^4/x,x=%plusInfinity)
>
> (18) 0
> Type:
> Union(OrderedCompletion(Expression(Integer)),...)
<snip>
> (21) -> limit(-x*Si(2*x/3)/x,x=3D%plusInfinity)
>
> %pi
> (21) - ---
> 2
> Type:
> Union(OrderedCompletion(Expression(Integer)),...)
> (22) -> limit(3/x,x=3D%plusInfinity)
>
> (22) 0
> Type:=20
> Union(OrderedCompletion(Fraction(Polynomial(Integer))),...)
>
> Is this a bug or just something not implemented?
I will check more details, but this looks more like unimplemented
thing. Limits are computed using few different methods.
For various reasons FriCAS will not split expression into parts,
it just checks if given method is applicable and then uses it.
Gruntz is most powerful when applicable, but (currently) can not
handle oscilating function. Si is probably handled by special
case for simple limits. '12*cos(x/3)^4/x' is probably handled
by 'generalized series' method, old somewhat ad-hoc code that
probably does not know about Si. Ideally Gruntz would be
extended to handle oscilating functions and special cases
would be transfered to it. In a sense it "just matter of
programming"...
--
Waldek Hebisch
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