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,
g:=integrate(sinc(x)*sinc(x/3),x)
x 4 x 2 4 x 2 x
12 cos(─) - 15 cos(─) + 2 x Si(───) - x Si(───) + 3
3 3 3 3
(4) ─────────────────────────────────
x
Type: Union(Expression(Integer),...)
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)),...)
(19) -> limit(-15*cos(x/3)^2/x,x=%plusInfinity)
(19) 0
Type:
Union(OrderedCompletion(Expression(Integer)),...)
(20) -> limit(2*x*Si(4*x/3)/x,x=%plusInfinity)
(20) %pi
Type:
Union(OrderedCompletion(Expression(Integer)),...)
(21) -> limit(-x*Si(2*x/3)/x,x=%plusInfinity)
%pi
(21) - ───
2
Type:
Union(OrderedCompletion(Expression(Integer)),...)
(22) -> limit(3/x,x=%plusInfinity)
(22) 0
Type:
Union(OrderedCompletion(Fraction(Polynomial(Integer))),...)
Is this a bug or just something not implemented?
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