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

From: Waldek Hebisch
Subject: Re: [Axiom-developer] The Gosper algorithm for sum of hypergeometric functions.
Date: Mon, 27 Nov 2006 17:37:33 +0100 (CET)

> Today I can't obtain sum as sum (1 / factorial n, n) with axiom silver.
> Is there someone who has already make a such package ?
> Is there someone who is working on ?
> This algorithm uses hypergeometric functions and a recursive relation
> over polynoms as a(n)p(n+1)-b(n-1)p(n)=c(n) where we are looking for
> one polynom p(n) from a(n), b(n) et c(n).
> I ask the same question : 
> Are there such packages already done ?
> Who is working for such packages ?

Axiom has implementation of Gosper algorithm -- look at package
GosperSummationMethod.  Unfortunatly, normally Axiom uses Gosper
method only for rational functions.  I played a bit with using
Gosper method for other functions but there are two problems here:

1) Gosper methods is applicable to hypergeometric terms. However, many
expression which "obviously" are hypergeometric terms does not look
like hypergeometric when you take their Axiom representation.
2) Many examples do not work because Axiom can not do needed algebraic
simplifications (famous sqrt(2)*sqrt(3)-sqrt(6) problem).

P.S.  I do not remember if there is a trick to use GospersMethod
from command line -- I probably had to modify and recompile some
algebra files.

                              Waldek Hebisch

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