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

**From**: |
Bill Page |

**Subject**: |
[Axiom-developer] [Axiom-mail] beginner question about sum(...) |

**Date**: |
Sun, 23 Jan 2005 13:21:59 -0600 |

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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