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BUILT-IN MATHEMATICA SYMBOL

DifferenceRootReduce

attempts to reduce expr to a single DifferenceRoot object as a function of n.

MORE INFORMATION

DifferenceRootReduce will attempt to represent any expression as a DifferenceRoot object.

DifferenceRootReduce always gives exactly when the DifferenceRoot object for expr is equivalent to the zero sequence.

DifferenceRootReduce automatically threads over lists, as well as equations and inequalities.

DifferenceRootReduce[f] operates on a pure function or pure DifferenceRoot object.

EXAMPLES

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Basic Examples (2)

Reduce the Fibonacci sequence to a DifferenceRoot object:

Compare the values:

Prove the Cassini identity:

Reduce the Fibonacci sequence to a DifferenceRoot object:

In[1]:=

Out[1]=

Compare the values:

In[2]:=

Out[2]=

In[3]:=

Out[3]=

Prove the Cassini identity:

In[1]:=

Out[1]=

Scope (8)

Polynomial functions:

Rational functions:

Hypergeometric terms:

Addition:

Termwise multiplication:

Multisection:

General expressions:

DifferenceRootReduce threads automatically over lists:

Options (1)

DifferenceRootReduce can give non-homogeneous equations:

Use the option Method

to get a homogeneous equation:

Applications (2)

A finite sum:

The difference equation shows that all the values at

are odd:

Define Padovan numbers:

Prove recurrence relations:

Prove summation identity: