Continued fractions

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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: <hankin.robin@gmail.com>

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

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# 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