SumTools[IndefiniteSum]
Rational
compute closed forms of indefinite sums of rational functions
Calling Sequence
Parameters
Description
Examples
References
Rational(f, k, options)
f
-
rational function in k
k
name
options
(optional) equation of the form failpoints=true or failpoints=false
The Rational(f, k) command computes a closed form of the indefinite sum of with respect to .
Rational functions are summed using Abramov's algorithm (see the References section). For the input rational function , the algorithm computes two rational functions and such that and the denominator of has minimal degree with respect to . The non-rational part, , is then expressed in terms of the digamma and polygamma functions.
If the option failpoints=true (or just failpoints for short) is specified, then the command returns a pair , where
is the closed form of the indefinite sum of w.r.t. ,
is a list containing the integer poles of , and
is a list containing the poles of and that are not poles of .
See SumTools[IndefiniteSum][Indefinite] for more detailed help.
The following expression is rationally summable.
Check the telescoping equation:
A non-rationally summable example.
Compute the fail points.
Indeed, is not defined at , and is not defined at .
Abramov, S.A. "Indefinite sums of rational functions." Proceedings ISSAC'95, pp. 303-308. 1995.
See Also
SumTools[IndefiniteSum][Indefinite]
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