The simple continued fraction is in the form
$$[1;1,2,3,4,5,\dots]=1+\cfrac{1}{1+\cfrac{1}{2+\cdots}}, $$ for instance. Obviously,the coefficients $x\_i$can be computed by computable function $x\_i=f(i), i\in \mathbb{N},$ and, $i$ is the $i$th coefficients.


Is there any function by which to compute coefficients of continued fraction of irrational algebraic non-quadritic number like $\sqrt[3]{5}$? Any example is appreciated.



Reference request for function by which to compute coefficients of continued fraction of algebaic number
This paper may be worth a look:


E. Bombieri and A. J. van der Poorten. Continued fractions of algebraic numbers. Computational algebra and number theory (Sydney, 1992), pp. 137–152. Kluwer Acad. Publ., 1995. 


Also, R.P. Brent, Alfred J. van der Poorten, Herman J.J. te Riele: A comparative study of algorithms for computing continued fractions of algebraic numbers" Algorithmic Number Theory (Talence, 1996), pages 35-47, Lecture Notes in Computer Science, 1122, Springer, Berlin, 1996.


