Overview - Maple Help

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).