contfrac-package {contfrac}R Documentation

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: <r.hankin@noc.soton.ac.uk>

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”

    Examples

      # 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
    

    [Package contfrac version 1.1-5 Index]