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SumTools[Hypergeometric][LowerBound] - compute a lower bound for the order of the telescopers for a hypergeometric term
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Calling Sequence
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LowerBound(T, n, k, En, 'Zpair')
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Parameters
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T
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hypergeometric term in 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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(optional) name denoting the shift operator with respect to n
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'Zpair'
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(optional) name
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Description
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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.
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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.
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Examples
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![with(SumTools[Hypergeometric])](/support/helpjp/helpview.aspx?si=5481/file06628/math117.png)
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Zeilberger's algorithm is not applicable to the following hypergeometric term so LowerBound returns an error.
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![L := Zpair[1]](/support/helpjp/helpview.aspx?si=5481/file06628/math170.png)
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The computed lower bound is 3, while the order of the minimal telescoper is
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References
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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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