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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
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
where \(\Delta_k\) is the k-forward difference operator, i.e., \(\Delta_k \left(t_k\right) \equiv t_{k+1} - t_k.\)
There are also verbose versions of the commands which are called by adding one of the following prefixes:
SummaryJust a summary at the end is shown
VerboseSome information in the intermediate steps
VeryVerboseMore information
ExtraEven more information including information on the linear system in Zeilberger’s algorithm
For example:
GosperVerbose, parGosperVeryVerbose,
ZeilbergerExtra, AntiDifferenceSummary.
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