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SumTools[IndefiniteSum][Rational] - compute closed forms of indefinite sums of rational functions
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Calling Sequence
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Rational(f, k, options)
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Parameters
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f
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rational function in k
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k
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name
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options
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(optional) equation of the form failpoints=true or failpoints=false
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Description
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The Rational(f, k) command computes a closed form of the indefinite sum of  with respect to  .
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If the option failpoints=true (or just failpoints for short) is specified, then the command returns a pair ![g, [p, q]](/support/helpjp/helpview.aspx?si=5464/file06644/math105.png) , where
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 is a list containing the integer poles of  , and
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Examples
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![with(SumTools[IndefiniteSum])](/support/helpjp/helpview.aspx?si=5464/file06644/math140.png)
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The following expression is rationally summable.
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Check the telescoping equation:
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A non-rationally summable example.
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Compute the fail points.
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![g, fp := -1/(n-5)-1/(n-4)+1/(n-3)+1/(n-2)+1/(n-1), [[0 .. 0, 3 .. 3, 5 .. 5], [1, 2, 4]]](/support/helpjp/helpview.aspx?si=5464/file06644/math204.png)
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Indeed,  is not defined at  , and  is not defined at  .
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References
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Abramov, S.A. "Indefinite sums of rational functions." Proceedings ISSAC'95, pp. 303-308. 1995.
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