Rational - Maple Help
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SumTools[IndefiniteSum]

  

Rational

  

compute closed forms of indefinite sums of rational functions

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Rational(f, k, options)

Parameters

f

-

rational function in k

k

-

name

options

-

(optional) equation of the form failpoints=true or failpoints=false

Description

• 

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.

Examples

The following expression is rationally summable.

(1)

(2)

Check the telescoping equation:

(3)

A non-rationally summable example.

(4)

(5)

(6)

Compute the fail points.

(7)

(8)

Indeed,  is not defined at , and  is not defined at .

References

• 

Abramov, S.A. "Indefinite sums of rational functions." Proceedings ISSAC'95, pp. 303-308. 1995.

See Also

SumTools[IndefiniteSum]

SumTools[IndefiniteSum][Indefinite]

 


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