SumTools[Hypergeometric][Zeilberger] - perform Zeilberger's algorithm
SumTools[Hypergeometric][ZeilbergerRecurrence] - construct the Zeilberger's recurrence
SumTools[Hypergeometric][Verify] - verify the result from Zeilberger's algorithm
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Calling Sequence
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Zeilberger(T, n, k, En)
Zeilberger(T, n, k, En, 'gosper')
ZeilbergerRecurrence(T, n, k, f, l..u)
Verify(T, 'Zpair', n, k, En)
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Parameters
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T
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hypergeometric term of n and k
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n
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name
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k
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name
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En
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name; denote the shift operator with respect to n
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f
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name of the recurrence function
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l..u
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range for k
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'Zpair'
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list of two elements specifying a Z-pair for T
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Description
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and a function such that
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En is the shift operator with respect to n, defined by .
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The algorithm has two implementations. The default implementation is based on the universal denominators, and another one uses a variant of Gosper's algorithm. With the 'gosper' option, Gosper-based implementation is used.
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The output from the Zeilberger command is a list of two elements representing the computed Z-pair .
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The Verify(T, 'Zpair', n, k, En) command verifies the correctness of the result ('Zpair') returned from Zeilberger, that is, it tries to verify that:
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Examples
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Maple returns an error if no Z-pair is found in the specified order range (by default ).
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Try Zeilberger's algorithm with order of L restricted to the range from to .
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References
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Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A K Peters, Ltd., 1996.
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Zeilberger, D. "The Method of Creative Telescoping." Journal of Symbolic Computing. Vol. 11. (1991): 195-204.
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