Overview of the LREtools[HypergeometricTerm] Subpackage - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : LREtools : HypergeometricTerm : LREtools/HypergeometricTerm

Overview of the LREtools[HypergeometricTerm] Subpackage

 

Calling Sequence

Description

List of LREtools[HypergeometricTerm] Commands

Examples

References

Calling Sequence

LREtools[HypergeometricTerm][command](arguments)

command(arguments)

Description

• 

The commands in the LREtools[HypergeometricTerm] subpackage solve the following problems.

1. 

Find polynomial solutions of a linear difference equation with polynomial coefficients depending on hypergeometric terms.

2. 

Find the hypergeometric dispersion of two polynomials depending on hypergeometric terms.

3. 

Find a solution of an orbit problem.

4. 

Find a universal denominator of the rational solutions of a linear difference equation with polynomial coefficients depending on hypergeometric terms.

5. 

Find rational solutions of a linear difference equation with polynomial coefficients depending on hypergeometric terms.

• 

Each command in the LREtools[HypergeometricTerm] subpackage 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 LREtools[HypergeometricTerm] subpackage is a module, it is also possible to use the form LREtools[HypergeometricTerm]:-command to access a command. For more information, see Module Members.

List of LREtools[HypergeometricTerm] Commands

• 

The following is a list of available commands.

AreSameSolution

HGDispersion

HypergeometricSolution

IsSolution

OrbitProblemSolution

PolynomialSolution

RationalSolution

SubstituteTerm

UniversalDenominator

 

 

 

• 

To display the help page for a particular LREtools[HypergeometricTerm] command, see Getting Help with a Command in a Package.

Examples

withLREtoolsHypergeometricTerm:

eqyn+2t+nyn+1+nt1yn

eq:=yn+2t+nyn+1+nt1yn

(1)

PolynomialSolutioneq,yn,t=n!

t_C1n,t,n+1

(2)

eqyn+11+n+1tyn1+t

eq:=yn+11+n+1tyn1+t

(3)

PolynomialSolutioneq,yn,t=n!

0,t,n+1

(4)

RationalSolutioneq,yn,t=n!

_C11+t,t,n+1

(5)

eq45yx9yxx18yx+3+9yx+3x

eq:=45yx9yxx18yx+3+9yx+3x

(6)

PolynomialSolutioneq,yx,t,91107x8x2

_C1x5,t,98x27x+10

(7)

px+2+22sx+100+e100v;qsx+sv+x;exts=2x,v=ex

p:=x+2+4se100v+x+100

q:=sx+sv+x

ext:=s=2x,v=ex

(8)

HGDispersionp,q,x,ext

100

(9)

References

  

Abramov, S.A., and Bronstein, M. "Hypergeometric dispersion and the orbit problem." Proc. ISSAC 2000.

  

Bronstein, M. "On solutions of Linear Ordinary Difference Equations in their Coefficients Field." INRIA Research Report. No. 3797. November 1999.

See Also

LREtools

LREtools[HypergeometricTerm][HGDispersion]

LREtools[HypergeometricTerm][PolynomialSolution]

LREtools[HypergeometricTerm][RationalSolution]

UsingPackages

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam