Continued Fractions

Various utilities for evaluating continued fractions.

Continued fractions in R

Continued fractions

A continued fraction is an expression of the form

Such expressions are interesting and useful in a number of mathematical applications. A generalized continued fraction is an expression of the form

The contfrac package provides functionality to deal with both these.

Installation

To install the most recent stable version on CRAN, use install.packages() at the R prompt:

R> install.packages("contfrac")

And then to load the package use library():

library("contfrac")

Package features

The package provides functionality for dealing with continued fractions.

as_cf(pi,n=7)   # convert pi to continued fraction form
#> [1]   3   7  15   1 292   1   1

We can evaluate convergents of any sequence using convergents() or nconv():

convergents(1:8)
#> $A
#> [1]     1     3    10    43   225  1393  9976 81201
#> 
#> $B
#> [1]     1     2     7    30   157   972  6961 56660
nconv(1:8)
#> [1] 1.433127

The package uses standard IEEE arithmetic so is not reliable past a certain point, shown here by expanding the golden ratio:

as_cf((1+sqrt(5))/2,n=50)
#>  [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
#> [39] 2 2 1 8 2 2 2 3 2 1 2 3

Further information

For more details, and some discussion of the mathematics of continued fractions, see the package vignette.