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

[Martin Rubey]

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