Overview of the gfun Package - Maple Programming Help

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Overview of the gfun Package

 

Calling Sequence

Description

List of gfun Package Commands

References

Calling Sequence

gfun[command](arguments)

command(arguments)

Description

• 

The gfun package provides tools for determining and manipulating generating functions.

• 

You can perform computations with generating functions defined by equations. For example, given two generating functions defined by linear differential equations with polynomial coefficients, there is a procedure to compute the differential equation satisfied by their product.

• 

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

  

As the underlying implementation of the gfun package is a module, it is also possible to use the form gfun:-command to access a command from the package. For more information, see Module Members.

List of gfun Package Commands

• 

The following is a list of available commands.

`diffeq*diffeq`

`diffeq+diffeq`

`rec*rec`

`rec+rec`

algebraicsubs

algeqtodiffeq

algeqtoseries

algfuntoalgeq

borel

cauchyproduct

diffeqtohomdiffeq

diffeqtorec

gftypes

guesseqn

guessgf

hadamardproduct

holexprtodiffeq

invborel

Laplace

listtoalgeq

listtodiffeq

listtohypergeom

listtolist

listtoratpoly

listtorec

listtoseries

Parameters

poltodiffeq

poltorec

ratpolytocoeff

rectodiffeq

rectohomrec

rectoproc

seriestoalgeq

seriestodiffeq

seriestohypergeom

seriestolist

seriestoratpoly

seriestorec

seriestoseries

• 

The following is a list of available commands for differential equations and recurrences.

`diffeq*diffeq`

`diffeq+diffeq`

`rec*rec`

`rec+rec`

algebraicsubs

algeqtodiffeq

algeqtoseries

algfuntoalgeq

borel

cauchyproduct

diffeqtohomdiffeq

diffeqtorec

hadamardproduct

holexprtodiffeq

invborel

Laplace

poltodiffeq

poltorec

ratpolytocoeff

rectodiffeq

rectohomrec

rectoproc

 

 

• 

There are different types of generating functions that you can manipulate using the gfun package, for example, ordinary (ogf) and exponential (egf) generating functions. For more information on the predefined generating function types, see gftypes.

• 

Given the first terms of the sequence, the gfun package also contains functions that help determine generating functions.  In some cases, this answer is explicit. However, in most cases, an explicit expression does not exist, and the answer is an equation (either algebraic or differential) satisfied by the generating function.

• 

The indexed names _C[0], _C[1],... are used by gfun to represent arbitrary constants. If such a name is given in the input, it might not be preserved during the computation.

• 

The following is a list of commands available for numbers and series.

guesseqn

guessgf

listtoalgeq

listtodiffeq

listtohypergeom

listtolist

listtoratpoly

listtorec

listtoseries

seriestoalgeq

seriestodiffeq

seriestohypergeom

seriestolist

seriestoratpoly

seriestorec

seriestoseries

• 

You can obtain information about computations by setting infolevel[gfun] to 1 through 5.

• 

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

References

  

Salvy, B., and Zimmermann, P. "GFUN: A Maple Package for the Manipulation of Generating and Holonomic Functions in One Variable". ACM Transactions on Mathematical Software. Vol. 20 No. 2. (1994): 163-177.

See Also

genfunc

gfun/Parameters

gfun[gftypes]

UsingPackages

with

 


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