 Overview of the SumTools Package - Maple Programming Help

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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][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

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).