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

[Bill Page]

Kostas,

My previous reply did not address the issue of the reason why
Axiom returns the sum unevaluated. Here is what I could find out:

On Sunday, January 23, 2005 11:08 AM you wrote:
> 
> I am trying to make Axiom evaluate sum(1/k^2, k=1..n).  It 
> returns the sum unevaluated.

I expect the reason that it returns unevaluated is because Axiom
is simply incomplete. For example Maple gives:

> sum(1/k^2, k=1..n);
                                      1   2
                     -Psi(1, n + 1) + - Pi 
                                      6    

Axiom does have the Polygamma function, so we can write:

(3) -> f1(n)==sum(1/k^2, k=1..n)
                                                                   Type:
Void
(4) -> f2(n)==-polygamma(1,n+1)+1/6*%pi^2
                                                                   Type:
Void
(5) -> f2(5)
   Compiling function f2 with type PositiveInteger -> DoubleFloat

   (5)  1.463611111111111
                                                            Type:
DoubleFloat
(6) -> f1(5)
   Compiling function f1 with type PositiveInteger -> Union(Fraction
      Polynomial Integer,Expression Integer)

        5269
   (6)  ----
        3600
                                          Type: Union(Expression
Integer,...)
(7) -> %::DFLOAT

   (7)  1.4636111111111112
                                                            Type:
DoubleFloat
(8) -> 

---------

Regards,
Bill Page.



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