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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.
Categories: Sums and products Share packages Package zeilberger
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:
SummaryJust a summary at the end is shown
VerboseSome information in the intermidiate 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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