# ContinuedFractionK

ContinuedFractionK[f,g,{i,imin,imax}]

represents the continued fraction .

ContinuedFractionK[g,{i,imin,imax}]

represents the continued fraction .

# Details and Options

• ContinuedFractionK uses the standard Wolfram Language iterator specification.
• The iteration variable i is treated as local, effectively using Block.
• The limits of ContinuedFractionK need not be numbers. They can be Infinity or symbolic expressions.
• The following options can be given:
•  Assumptions \$Assumptions assumptions to make about parameters GenerateConditions False whether to generate conditions on parameters Method Automatic method to use VerifyConvergence True whether to verify convergence

# Examples

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## Basic Examples(2)

A simple continued fraction:

The convergents of a continued fraction:

## Options(1)

### GenerateConditions(1)

Generate conditions required for the continued fraction to converge:

## Properties & Relations(2)

A continued fraction can be constructed as a ratio of solutions to a second-order recurrence equation:

A continued fraction is the ratio of two linearly independent solutions:

ContinuedFractionK and FromContinuedFraction are reciprocals of one another:

## Possible Issues(1)

Continued fractions may not be convergent:

## Neat Examples(1)

Create a gallery of continued fractions:

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

#### Text

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

#### CMS

Wolfram Language. 2008. "ContinuedFractionK." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ContinuedFractionK.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_continuedfractionk, author="Wolfram Research", title="{ContinuedFractionK}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ContinuedFractionK.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_continuedfractionk, organization={Wolfram Research}, title={ContinuedFractionK}, year={2008}, url={https://reference.wolfram.com/language/ref/ContinuedFractionK.html}, note=[Accessed: 14-September-2024 ]}