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][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][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][MinimalZpair]
,
SumTools[Hypergeometric][Zeilberger]
,
SumTools[Hypergeometric][ZeilbergerRecurrence]
,
SumTools[Hypergeometric][ZpairDirect]
-
SumTools[Hypergeometric][DefiniteSum]
,
SumTools[Hypergeometric][IndefiniteSum]
,
SumTools[Hypergeometric][WZMethod]
-
SumTools[Hypergeometric][AreSimilar]
,
SumTools[Hypergeometric][ConjugateRTerm]
,
SumTools[Hypergeometric][IsHolonomic]
,
SumTools[Hypergeometric][IsHypergeometricTerm]
,
SumTools[Hypergeometric][IsProperHypergeometricTerm]
,
SumTools[Hypergeometric][Verify]
See Also
LREtools
,
rsolve
,
sum
,
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).