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zeilberger
is an implementation of Zeilberger’s algorithm
for definite hypergeometric summation, and also
Gosper’s algorithm for indefinite hypergeometric
summation.
zeilberger
makes use of the "filtering" optimization method developed by Axel Riese.
zeilberger
was developed by Fabrizio Caruso.
load ("zeilberger")
loads this package.
zeilberger
implements Gosper’s algorithm for indefinite hypergeometric summation.
Given a hypergeometric term F_k in k we want to find its hypergeometric
anti-difference, that is, a hypergeometric term f_k such that
F_k = f_(k+1) - f_k.
zeilberger
implements Zeilberger’s algorithm for definite hypergeometric summation.
Given a proper hypergeometric term (in n and k)
F_(n,k)
and a positive integer d we want to find a d-th order linear
recurrence with polynomial coefficients (in n) for
F_(n,k)
and a rational function R in n and k such that
a_0 F_(n,k) + ... + a_d F_(n+d),k = Delta_k(R(n,k) F_(n,k)),
where Delta_k is the k-forward difference operator, i.e., Delta_k(t_k) := t_(k+1) - t_k.
There are also verbose versions of the commands which are called by adding one of the following prefixes:
Summary
Just a summary at the end is shown
Verbose
Some information in the intermediate steps
VeryVerbose
More information
Extra
Even more information including information on the linear system in Zeilberger’s algorithm
For example:
GosperVerbose
, parGosperVeryVerbose
,
ZeilbergerExtra
, AntiDifferenceSummary
.
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