[Axiom-developer] Re: [Axiom-mail] beginner question about sum(...)

[Kostas Oikonomou]

Hello Martin,

I was thinking about this a bit more.  If  "a" is a positive integer, of course 
the sum
1/(k*(k+a)) is hypergeometric. And indeed Axiom evaluates it if you give "a" a 
positive
integral value.  Now wouldn't you expect that if you declared "a" to be a 
positive integer
the summation would be evaluated?  It is not.  Instead Axiom says that "a" has 
not been
given a value.

A short while ago, Bill Page also posted a message about this general 
situation.  That if
you make a certain type declaration, you would expect Axiom to act accordingly, 
but it
does not appear to do so.

Regards,

                                Kostas

> Dear Kostas,
>
> Kostas Oikonomou writes:
>  >
>  > But I was disappointed by the sum(1/k^2, k=1..n) example.  I saw that
>  > Gosper's method is implemented in sum.spad.pamphlet, but this (rather
>  > simple) sum needs symbolic manipulation of gamma and psi functions, which is
>  > not there.  More generally, special functions seem to be handled only
>  > numerically.  At least for my prospective use of Axiom, this points to a
>  > rather big "hole". And I wonder how many others of this sort there are.
>  >
>  > I also tried sum(1/(k*(k+a)), k=1..n).  That was also returned unevaluated,
>  > although Gosper's method should handle it.
>
> Why should Gosper's method handle it? As far as I can see the solution is not
> hypergeometric?
>
>
> Martin