16 Mar
2019
16 Mar
'19
9:53 p.m.
Re continued fraction expansions (CFE's) defined via: Given x in (0, 1), let c(1) = floor(1/x); x(1) = frac(1/x) (= 1/x - floor(1/x)) ... ... c(n+1) = floor(1/x(n)) x(n+1) = frac(1/x(n)) ... Then the integer sequence (c(1), c(2), ..., c(n), ...) is the cfe of x. Question: --------- Are there algorithms relating the cfe of x with the cfe of simple functions of x like f(x) = Kx (K a real constant) f(x) = x + K f(x) = x^p (p > 0) f(x) = log(1/x) f(x) = e^x ??? —Dan