Overview of the SumTools Package

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	Calling Sequence
	SumTools[command](arguments) command(arguments)

Description

•	The SumTools package contains commands that help find closed forms of definite and indefinite sums. The package consists of three commands and three subpackages.

•	Each command in the SumTools package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

•	To display the help page for a particular SumTools command, see Getting Help with a Command in a Package.

Commands for Computing Closed Forms of Definite and Indefinite Sums

•	SumTools[Summation]: compute closed forms of definite and indefinite sums

•	SumTools[DefiniteSummation]: compute closed forms of definite sums

•	SumTools[IndefiniteSummation]: compute closed forms of indefinite sums

Tools for Computing Closed Forms of Indefinite sums: The IndefiniteSum Subpackage

•	SumTools[IndefiniteSum][AccurateSummation]: compute indefinite sums using the method of accurate summation

•	SumTools[IndefiniteSum][AddIndefiniteSum]: library extension mechanism

•	SumTools[IndefiniteSum][HomotopySum]: compute indefinite sums of expressions containing unspecified functions

•	SumTools[IndefiniteSum][Hypergeometric]: compute indefinite sums of hypergeometric terms

•	SumTools[IndefiniteSum][Indefinite]: compute closed forms of indefinite sums

•	SumTools[IndefiniteSum][Polynomial]: compute indefinite sums of polynomials

•	SumTools[IndefiniteSum][Rational]: compute indefinite sums of rational functions

•	SumTools[IndefiniteSum][RemoveIndefiniteSum]: library extension mechanism

Tools for Computing Closed Forms of Definite Sums: The DefiniteSum Subpackage

•	SumTools[DefiniteSum][CreativeTelescoping]: compute closed forms of definite sums using the creative telescoping method

•	SumTools[DefiniteSum][Definite]: compute closed forms of definite sums

•	SumTools[DefiniteSum][pFqToStandardFunctions]: compute closed forms of definite sums using the conversion method where the hypergeometric series is used as an intermediate representation

•	SumTools[DefiniteSum][SummableSpace]: compute all sequences satisfying a given first order recurrence that are summable by either Gosper's algorithm or the accurate summation algorithm

•	SumTools[DefiniteSum][Telescoping]: compute closed forms of definite sums using the classical telescoping method

Tools for Working with Hypergeometric Terms: The Hypergeometric Subpackage

•	Normal forms of rational functions and hypergeometric terms:

SumTools[Hypergeometric][EfficientRepresentation],

SumTools[Hypergeometric][MultiplicativeDecomposition],

SumTools[Hypergeometric][PolynomialNormalForm],

SumTools[Hypergeometric][RationalCanonicalForm],

SumTools[Hypergeometric][RegularGammaForm],

SumTools[Hypergeometric][SumDecomposition]

•	Algorithms for definite and indefinite sums of hypergeometric type:

SumTools[Hypergeometric][ExtendedGosper],

SumTools[Hypergeometric][ExtendedZeilberger],

SumTools[Hypergeometric][Gosper],

SumTools[Hypergeometric][IsZApplicable],

SumTools[Hypergeometric][KoepfGosper],

SumTools[Hypergeometric][KoepfZeilberger],

SumTools[Hypergeometric][LowerBound],

SumTools[Hypergeometric][MinimalTelescoper],

SumTools[Hypergeometric][MinimalZpair],

SumTools[Hypergeometric][Zeilberger],

SumTools[Hypergeometric][ZeilbergerRecurrence],

SumTools[Hypergeometric][ZpairDirect]

•	Applications:

SumTools[Hypergeometric][DefiniteSum],

SumTools[Hypergeometric][IndefiniteSum],

SumTools[Hypergeometric][WZMethod]

•	Other functions:

SumTools[Hypergeometric][AreSimilar],

SumTools[Hypergeometric][ConjugateRTerm],

SumTools[Hypergeometric][BottomSequence],

SumTools[Hypergeometric][IsHolonomic],

SumTools[Hypergeometric][IsHypergeometricTerm],

SumTools[Hypergeometric][IsProperHypergeometricTerm],

SumTools[Hypergeometric][Verify]

	See Also
	LREtools, rsolve, sum, sumtools, UsingPackages, with

References

Abramov, S.A.; Carette, J.J.; Geddes, K.O.; and Le, H.Q. "Symbolic Summation in Maple." Technical Report CS-2002-32, School of Computer Science, University of Waterloo, Ontario, Canada. (2002).

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