This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

DifferenceRoot

 DifferenceRoot[lde] represents a function that solves the linear difference equation specified by .
• DifferenceRoot[lde][s] finds the value of the solution to the difference equation at the specific point s.
• DifferenceRoot[lde][{s1, s2, ...}], etc. threads automatically over lists.
Reduce combinations of special sequences to their DifferenceRoot form:
Use f like any sequence:
Define a new sequence using DifferenceRoot directly:
Use it like any sequence:
Prove properties:
Several functions can produce closed-form answers by using DifferenceRoot functions:
Reduce combinations of special sequences to their DifferenceRoot form:
 Out[1]=
Use f like any sequence:
 Out[2]=
 Out[3]=

Define a new sequence using DifferenceRoot directly:
Use it like any sequence:
 Out[2]=
Prove properties:
 Out[3]=

Several functions can produce closed-form answers by using DifferenceRoot functions:
 Out[1]=
 Out[2]=
 Out[3]=
 Scope   (10)
Evaluate at an arbitrary point:
DifferenceRoot works on rational coefficients:
Homogeneous linear recurrences:
Inhomogeneous linear recurrences:
Multiple initial values:
Solutions of a difference equation:
A result from Sum:
Coefficients in the expansion of a function:
Formula of a sequence:
Equations with holonomic constant terms are automatically lifted to polynomial coefficients:
 Applications   (1)
Define Pell numbers:
Closed form formula:
Identity analogous to Cassini's identity:
A summation identity:
Use DifferenceRootReduce to generate DifferenceRoot objects:
Get the corresponding ordinary difference equation:
Use the equation to verify solutions:
Sum of a DifferenceRoot object:
Find the generating function of a DifferenceRoot object:
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