contFracR (version 1.2.1)

root2cfrac: Function To Generate Continued Fraction For Arbitrary Roots

Description

This function generates the generalized continued fraction for any input value x^(m/n).

Usage

root2cfrac(x, n, m = 1, nterms = 10, ...)

Value

A list, containing: The continued fraction numerators and denominators in bigz form num , denom . The continued fraction numerators and denominators in numeric form numericnum, numericdenom . In the extreme case that a value exceeds the machine size of a numeric, NA is returned. The inputs x, n, m are echoed back.

Arguments

x

The number itself. Integers, doubles, bigz, and bigq classes are allowed.

n

The integer denominator of the power to which x is raised. That is, when m is 1, the n-th root of x is generated.

m

The integer numerator of the power to which x is raised. The default is 1.

nterms

How many terms (denominators) to calculate.

...

Reserved for future use

Author

Carl Witthoft,

Details

The generalized continued fraction for arbitrary roots will not be periodic, and may not even show a pattern in the denominator values. By comparison, sqrt2periodicCfrac generates a simple continued fraction with a periodic sequence for square roots only. That periodic sequence tends to converge more slowly than the aperiodic sequence produced here.

References

https://en.wikipedia.org/wiki/Generalized_continued_fraction

See Also

sqrt2periodicCfrac, cfrac2num

Examples

root2cfrac(x = 2, n = 3)
root2cfrac(x=17, n= 5, m= 2)
root2cfrac(x = 2, n = 2, nterms = 20)
#compare with 
sqrt2periodicCfrac(num = 2, nterms = 20)