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SumTools[Hypergeometric][LowerBound] - compute a lower bound for the order of the telescopers for a hypergeometric term
Calling Sequence
LowerBound(T, n, k, En, 'Zpair')
Parameters
T
-
hypergeometric term in n and k
n
name
k
En
(optional) name denoting the shift operator with respect to n
'Zpair'
(optional) name
Description
Let T be a hypergeometric term in n and k. The function LowerBound(T, n, k) computes a lower bound for the order of the telescopers for T if it is guaranteed that Zeilberger's algorithm is applicable to T.
If the fourth and the fifth optional arguments (each of which can be any name), En and 'Zpair' respectively, are specified, the minimal telescoper for T is computed and assigned to the fifth argument 'Zpair' using the computed lower bound as the starting value of the guessed orders.
Examples
Zeilberger's algorithm is not applicable to the following hypergeometric term so LowerBound returns an error.
Error, (in SumTools:-Hypergeometric:-LowerBound) Zeilberger's algorithm is not applicable
The computed lower bound is 3, while the order of the minimal telescoper is
See Also
SumTools[Hypergeometric], SumTools[Hypergeometric][IsZApplicable], SumTools[Hypergeometric][MinimalZpair], SumTools[Hypergeometric][Zeilberger], SumTools[Hypergeometric][ZpairDirect]
References
Abramov, S.A. and Le, H.Q. "A Lower Bound for the Order of Telescopers for a Hypergeometric Term." CD-ROM. Proceedings FPSAC 2002. (2002).
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