PolynomialSolution - Maple Help
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LREtools[HypergeometricTerm]

  

PolynomialSolution

  

return the polynomial solution of linear difference equation depending on a hypergeometric term

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

PolynomialSolution(eq, var, term)

Parameters

eq

-

linear difference equation depending on a hypergeometric term

var

-

function variable for which to solve, for example, z(n)

term

-

hypergeometric term

Description

• 

The PolynomialSolution(eq, var, term) command returns the polynomial solution of the linear difference equation eq. If such a solution does not exist, the function returns NULL.

• 

The hypergeometric term in the linear difference equation is specified by a name, for example, t. The meaning of the term is defined by the parameter term. It can be specified directly in the form of an equation, for example, , or specified as a list consisting of the name of term variable and the consecutive term ratio, for example, .

• 

If the third parameter is omitted, then the input equation can contain a hypergeometric term directly (not a name). In this case, the procedure extracts the term from the equation, transforms the equation to the form with a name representing a hypergeometric term, and then solves the transformed equation.

• 

The term "polynomial solution" means a solution  in  , that is, in the form  where  and  are in .

• 

The solution is the function, corresponding to var. The solution involves arbitrary constants of the form, for example, _c1 and _c2.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

References

  

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

See Also

LREtools[HypergeometricTerm]

LREtools[HypergeometricTerm][RationalSolution]

LREtools[HypergeometricTerm][SubstituteTerm]

 


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