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## Re: [Axiom-developer] The Gosper algorithm for sum of hypergeometric fun

**From**: |
Martin Rubey |

**Subject**: |
Re: [Axiom-developer] The Gosper algorithm for sum of hypergeometric functions. |

**Date**: |
27 Nov 2006 17:25:19 +0100 |

**User-agent**: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |

Francois Maltey <address@hidden> writes:
>* Hello, *
>* *
>* Today I can't obtain sum as sum (1 / factorial n, n) with axiom silver.*
As far as I know, this sum is not "Gosperable". It is doable by Zeilberger's
algorithm.
Zeilberger is not implemented in Axiom. However, you can use my guessing
package to guess a recurrence. Unfortunately, you have no way to know how many
terms you have to plug in.
Sample session: (PRec is for Polynomially RECursive)
(7) -> guessPRec([reduce(+, [factorial i for i in 1..n]) for n in 1..8])
(7) []
Type: List Record(function: Expression Integer,order: NonNegativeInteger)
(8) -> guessPRec([reduce(+, [factorial i for i in 1..n]) for n in 1..9])
(8)
[
[
function =
[f(n): - f(n + 2) + (n + 4)f(n + 1) + (- n - 3)f(n)= 0,f(0)= 1,f(1)= 3]
,
order= 0]
]
Type: List Record(function: Expression Integer,order: NonNegativeInteger)
To obtain the guessing package, send me a note. The version on MathAction is
OK, but contains one or two bugs (irrelevant for most things)
Martin