After an unsuccessful month attempting to get Axiom to sum an elemental infinite series, I am joining my first newsgroup to ask if Axiom is able to do it. Here are some ways I have found not to get the correct result:
(3) -> sum(x**n/n, n=1..%plusInfinity)
There are 6 exposed and 2 unexposed library operations named sum
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op sum
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named sum
with argument type(s)
_expression_(Integer)
SegmentBinding(OrderedCompletion(Integer))
Perhaps you should use @ to indicate the required return type, or
$ to specify which version of the function you need.
(3) -> limit(sum(x**n/n, n=1..k), k=%plusInfinity)
(3) "failed"
Type: Union("failed",...)
(4) ->
Of the open source CAS I've tried, only Sympy has been able to sum this infinite series. I am using Mathematica and Maple out of desperation. If I want to prove the correctness of their results, I can't, because their methods are trade secrets.