# contfrac-package: Continued fractions In contfrac: Continued Fractions

## Description

Various utilities for manipulating continued fractions

## Details

 Package: contfrac Type: Package Version: 1.0 Date: 2008-04-04 License: GPL

## Author(s)

Robin K. S. Hankin

Maintainer: <[email protected]>

## References

• W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling 1992. Numerical recipes 3rd edition: the art of scientific computing. Cambridge University Press; section 5.2 “Evaluation of continued fractions”

• W. J. Lenz 1976. Generating Bessel functions in Mie scattering calculations using continued fractions. Applied Optics, 15(3):668-671

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# approximate real numbers with continued fraction: as_cf(pi) as_cf(exp(1),25) # OK up to element 21 (which should be 14) # Some convergents of pi: jj <- convergents(c(3,7,15,1,292)) jj\$A / jj\$B - pi # An identity of Euler's: jj <- GCF(a=seq(from=2,by=2,len=30), b=seq(from=3,by=2,len=30), b0=1) jj - 1/(exp(0.5)-1) # should be small # Now a continued fraction representation of tan(z): tan_cf <- function(z,n=14){ GCF(c(z,rep(-z^2,n-1)), seq(from=1,by=2,len=n)) } tan_cf(1+1i) - tan(1+1i) # should be small ```

contfrac documentation built on July 9, 2017, 9:01 a.m.