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SumTools[Hypergeometric][EfficientRepresentation] - construct the four efficient representations of a hypergeometric term
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Calling Sequence
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EfficientRepresentation[1](H, n)
EfficientRepresentation[2](H, n)
EfficientRepresentation[3](H, n)
EfficientRepresentation[4](H, n)
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Parameters
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H
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hypergeometric term of n
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n
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variable
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Description
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Let H be a hypergeometric term of n. The EfficientRepresentation[i](H,n) calling sequence constructs the ith efficient representation of H of the form  where alpha is a constant,  is a product of Gamma-function values and their reciprocals. Additionally,
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1.
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 has the minimal number of factors,
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2.
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 is a rational function which is minimal in one sense or another, depending on the particular rational canonical form chosen to represent the certificate of  .
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If  then  is minimal;
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if  then  is minimal;
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If EfficientRepresentation is called without an index, the first efficient representation is constructed.
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Examples
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![with(SumTools[Hypergeometric])](/support/helpjp/helpview.aspx?si=5469/file06618/math130.png)
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](/support/helpjp/helpview.aspx?si=5469/file06618/math141.png)
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](/support/helpjp/helpview.aspx?si=5469/file06618/math148.png)
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](/support/helpjp/helpview.aspx?si=5469/file06618/math155.png)
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](/support/helpjp/helpview.aspx?si=5469/file06618/math162.png)
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| (5) |
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| (6) |
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References
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Abramov, S.A.; Le, H.Q.; and Petkovsek, M. "Rational Canonical Forms and Efficient Representations of Hypergeometric Terms." Proc. ISSAC'2003, pp. 7-14. 2003.
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