# DifferenceRootReduce

DifferenceRootReduce[expr,n]

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

# Examples

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## Basic Examples(2)

Reduce the Fibonacci sequence to a DifferenceRoot object:

Compare the values:

Prove the Cassini identity:

## Scope(8)

Polynomial functions:

Rational functions:

Hypergeometric terms:

Addition:

Term-wise multiplication:

Multisection:

General expressions:

DifferenceRootReduce threads automatically over lists:

## Options(1)

### Method(1)

DifferenceRootReduce can give non-homogeneous equations:

Use the option Method->"Homogeneous" to get a homogeneous equation:

## Applications(3)

Verify the negation formula for Fibonacci:

Addition formula:

Double-angle formula:

Successor relation:

Conjugation relation:

A finite sum:

The difference equation shows that all the values at are odd:

Define Padovan numbers:

Prove recurrence relations:

Prove summation identity:

Wolfram Research (2008), DifferenceRootReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/DifferenceRootReduce.html (updated 2020).

#### Text

Wolfram Research (2008), DifferenceRootReduce, Wolfram Language function, https://reference.wolfram.com/language/ref/DifferenceRootReduce.html (updated 2020).

#### CMS

Wolfram Language. 2008. "DifferenceRootReduce." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2020. https://reference.wolfram.com/language/ref/DifferenceRootReduce.html.

#### APA

Wolfram Language. (2008). DifferenceRootReduce. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DifferenceRootReduce.html

#### BibTeX

@misc{reference.wolfram_2024_differencerootreduce, author="Wolfram Research", title="{DifferenceRootReduce}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/DifferenceRootReduce.html}", note=[Accessed: 18-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_differencerootreduce, organization={Wolfram Research}, title={DifferenceRootReduce}, year={2020}, url={https://reference.wolfram.com/language/ref/DifferenceRootReduce.html}, note=[Accessed: 18-July-2024 ]}