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Overview of the SumTools Package
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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