LREtools[HypergeometricTerm][PolynomialSolution] - return the polynomial solution of linear difference equation depending on a hypergeometric term
|
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 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.
|
|
|
Download Help Document
Was this information helpful?